tag:blogger.com,1999:blog-46366731143016807682024-03-14T00:07:19.026-07:00Breathe. Cry. Math.Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.comBlogger34125tag:blogger.com,1999:blog-4636673114301680768.post-79274399785310116742014-06-05T09:12:00.001-07:002014-06-05T09:12:28.699-07:00SP#7: Unit K Concept 10<div class="separator" style="clear: both; text-align: center;">
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This goes over how to write a repeating decimal as a rational number using geometric series. Make sure to use the infinite geometric series. The answer must be written as a fraction.</div>
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Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-19205513533229553232014-06-04T23:26:00.000-07:002014-06-06T23:04:43.442-07:00BQ #7 - Unit V<span style="background-color: white;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 13px; line-height: 18.200000762939453px;">1. Where does the difference quotient come from?</span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.200000762939453px;" /><span style="font-family: Arial, Helvetica, sans-serif; font-size: 13px; line-height: 18.200000762939453px;"><br /></span><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.200000762939453px;"></span><span style="font-family: Arial, Helvetica, sans-serif; font-size: 13px; line-height: 18.200000762939453px;">-First you need to know that the difference quotient is known as finding the slope of the tangent line to a graph. On this graph, f(x), we're given a point on the line, which will be <b><i>(x, f(x))</i></b>. If we move to a different point, then that will be delta x, or <i style="font-weight: bold;">h, </i>for that matter. The new placing of the point, is the total value of <i style="font-weight: bold;">x plus h. </i>So at this new point, the values will be (x+h, f(x+h)), which, if you connect to the value (x, f(x)), will create a secant line. Given these points, we can find the slope of the secant line using the formula (<i style="font-weight: bold;">y^2-y^1)/(x^2-x^1).</i> We then insert the numbers that correspond with the formula, which will look like this: <i style="font-weight: bold;">f(x+h)-f(x)/ x+h-x</i>. If you then simplify, you get the difference quotient: <i style="font-weight: bold;">f(x+h)-f(x)/b</i>. Through the process of finding the slope of a secant line, we also find the slope of the tangent line, or the difference quotient.</span></span><br />
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<span style="background-color: white;"><u style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.200000762939453px;">Source:</u><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.200000762939453px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18.200000762939453px;">1. http://cis.stvincent.edu/carlsond/ma109/DifferenceQuotient_images/IMG0470.JPG</span></span>Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-51320223967278266332014-05-16T13:28:00.003-07:002014-05-19T22:33:57.304-07:00BQ#6 – Unit U Concepts 1-81. What is continuity?<br />
Continuity is a way to describe a function that is predictable. It has no breaks, jumps, or holes. This kind of function can be drawn on a graph without lifting your pencil. In addition, the value is the same as the limit.<br />
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What is discontinuity?<br />
Discontinuity is a way to describe a function that is not predictable. There are two families: removable and non-removable discontinuities.<br />
A point discontinuity is a removable discontinuity. Here the limit exists wherever the open circle is. This looks like a hole on the graph. Sometimes the value and the limit might not be at the same point. In this case, it is as if you and your friend plan to go to the mall and show up there, but it burned down.<br />
In a non-removable discontinuity, the limit does not exist (NOT "there is no limit"). This includes a jump discontinuity where the graph is different coming from left and right. In this case, it is as if you and your friend plan to meet at a restaurant, but you two show up at different ones. Oscillating behavior has no limit and the value is undefined because it is simply oscillating and appears wiggly on a graph. In an infinite discontinuity (unbounded behavior) has vertical asymptote. This means it increases or decreases without bound toward infinity or negative infinity.<br />
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2. What is a limit?<br />
A limit is the intended height of a function. We read a limit as: "The limit as x approaches 'a number' of f(x) is equal to 'L.'" You can have an infinite amount of limits on a graph.<br />
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When does a limit exist?<br />
The limit exists in continuous functions. This is when the intended is the actual height also. However, we must understand that the function is not the value. The three times a limit does not exist are when we have non-removable discontinuities. When it 'DNE,' we must also right the reasons. If it was a jump discontinuity, the graph is different left and right. If it was an infinite discontinuity, it has unbounded behavior. If it is oscillating, the graph is simply oscillating and we cannot find its value either which means it is undefined.<br />
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What is the difference between a limit and a value?<br />
The limit is the intended height of the graph. Often this can be seen with two open circles or an open and closed circle. The value is the actual height. This is shown with a closed circle.<br />
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3. How do we evaluate limits numerically, graphically, and algebraically?<br />
We can evaluate limits numerically which is on a table. The tables I have drawn in the pictures show how we can get really really really really close to a number without actually touching it.<br />
Evaluating limits on a graph involves an actual graph. You put two fingers on the left and right side of where you want to evaluate a limit. If your fingers do not touch, the limit DNE.<br />
Algebraically, you should first try the direct substitution method. We can get a number, 0 over a number which is 0, a number over 0 which means the limit DNE, or 0/0 which is the indeterminate form. If you get 0/0, use another method because it is "not yet determined" and we need to keep on working to find the answer. Whatever number the x approaches, you plug that into any variable of the equation given. You can also try the rationalizing/conjugate method. Here you can use either the conjugate of the denominator or the numerator. You need to rearrange the equation given though by multiplying the top and bottom by the conjugate of either the numerator or denominator. Whichever conjugate you used, simplify it by FOILing. The non-conjugate will be left alone, so you can cancel things out. Remember, "...if something cancels, then your graph will have a HOLE!"Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-37470686189409482482014-04-24T04:06:00.004-07:002014-04-24T04:06:52.427-07:00BQ#4 – Unit T Concept 3<span style="font-family: Georgia, Times New Roman, serif; font-size: large;">Why is a “normal” tangent graph uphill, but a “normal” COtangent graph downhill? Use unit circle ratios to explain.</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">Tangent and cotangent are opposites of each other. Tangent=sin/cos. Whenever cos=0, tan is undefined because there would have to be asymptotes. The graph would go in a positive direction since they are positive in Quadrant 1 and Quadrant 3. Cotangent= cos/sin. Cotangent is positive in Quadrant 1 and Quadrant 3 as well. The asymptote begins at (0,0) where Quadrant 1 is.</span>Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-4796628322476976452014-04-24T03:56:00.001-07:002014-04-24T03:56:14.898-07:00BQ#3 – Unit T Concepts 1-3<span id="docs-internal-guid-a9931904-8af8-24a9-0701-f0c112c21408"></span><br />
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<span style="background-color: white; color: black; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: Georgia, Times New Roman, serif; font-size: large;">How do the graphs of sine and cosine relate to each of the others? Emphasize asymptotes in your response.</span></span></div>
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<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; font-size: 15px; line-height: 1; white-space: pre-wrap;">Tangent?</span><div>
<span style="font-family: Georgia, Times New Roman, serif;"><span style="font-size: 15px; line-height: 15px; white-space: pre-wrap;">Tangent is equal to sin/cos. It is undefined when cos=0. When sin=0, tangent goes through the x-axis since tan=0.</span></span></div>
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<br /><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; font-size: 15px; line-height: 1; white-space: pre-wrap;">Cotangent?</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="font-size: 15px; line-height: 15px; white-space: pre-wrap;">Cotangent is equalled to cos/sin. In Quadrant 1, t will be positive since the sin and cos graphs are positive. If the sin=1, cotangent will have asymptotes. In Quadrant 2, cos is negative; sin is positive. In quadrant 3, cos is negative; sin is negative. Their signs cancel out to make a positive cotangent. In Quadrant 4, cos is positive; sin is negative. This will give cotangent a negative answer.</span></span></div>
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<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; font-size: 15px; line-height: 1; white-space: pre-wrap;">Secant?</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="font-size: 15px; line-height: 15px; white-space: pre-wrap;">The reciprocal of secant is 1/cos. If cos=0, sec is undefined and will not touch. However, if the cos=1, sec amplitudes will touch.</span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="font-size: 15px; line-height: 15px; white-space: pre-wrap;"><br /></span></span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; font-size: 15px; white-space: pre-wrap;">Cosecant?</span><ul style="margin-bottom: 0pt; margin-top: 0pt;"><ul style="margin-bottom: 0pt; margin-top: 0pt;"><ul style="margin-bottom: 0pt; margin-top: 0pt;">
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<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; font-size: 15px; white-space: pre-wrap;">The reciprocal of cosecant is 1/sin. If sin=0, cosecant is undefined and will not touch. However, if sin=1, csc amplitudes will touch.</span></div>
Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-5930090570146308482014-04-18T01:19:00.001-07:002014-04-18T01:19:10.466-07:00BQ#5 – Unit T Concepts 1-3<span id="docs-internal-guid-62d5e045-73d9-70d5-4ff1-523c5ae3062f"></span><br />
<span style="background-color: white; white-space: pre-wrap;"><span style="font-family: Times, Times New Roman, serif; font-size: large;">Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use unit circle ratios to explain.</span></span><div>
<span style="background-color: white; font-family: Arial; font-size: 15px; white-space: pre-wrap;">The Unit Circle has ratios for trig functions. Sin=y/r, cos=x/r, tan=y/x, csc=r/y, sec=r/x, and cot=x/y. The asymptote is only present when the denominator is equal to 0. However, since r is always equal to 1 in the Unit Circle triangles, this will give us an actual number value for sine and cosine. For us to have an asymptote, we would have to have an undefined answer like in the other four trig graphs give us.</span></div>
Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-1622866192884896452014-04-16T22:37:00.001-07:002014-04-16T22:37:15.342-07:00BQ#2 – Unit T Concept Intro<span id="docs-internal-guid-62d5e045-692f-690b-02e1-386331d3507a"></span><br />
<span style="background-color: white; font-family: Arial; line-height: 1; white-space: pre-wrap;"><span style="font-size: large;">How do the trig graphs relate to the Unit Circle?</span><span style="font-size: 15px;"><br /></span></span><span style="font-family: Arial; font-size: 15px; line-height: 1; white-space: pre-wrap;">ANSWER: Trig graphs relate to the Unit Circle because we just have to imagine the Unit Circle being "unwrapped" into a straight line. This would be like the x-axis of the trig graphs. We have to imagine the Unit Circle still having its coordinates.</span><div>
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<li><span style="background-color: white; font-family: Arial; line-height: 1; white-space: pre-wrap;"><span style="font-size: large;">Period? - Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?</span></span></li>
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<span style="font-family: Arial; font-size: 15px; line-height: 15px; white-space: pre-wrap;">ANSWER: The period of sine and cosine is 2pi because of their positives and negatives. From quadrant one through four, sine is positive, positive, negative, negative. We imagine sine on the unit circle in portions. At 0* it is 0. At 90* it is 1. At 180* it is 0. At 270* it is -1. At 360* it is 0. These are literally the points on the graph that give sine a mountain-to-valley image. For cosine it is reflected, so we start with a valley then turn into a mountain. For tangent and cotangent, the signs from quadrant one to four are positive, negative, positive, negative. Within this "unwrapped unit circle" we only see two periods. However, this kind of graph only shows us half of the period, hence, it is pi.</span></div>
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<li><span style="background-color: white; font-family: Arial; line-height: 1; white-space: pre-wrap;"><span style="font-size: large;">Amplitude? – How does the fact that sine and cosine have amplitudes of one (and the other trig functions don’t have amplitudes) relate to what we know about the Unit Circle?</span></span></li>
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<span style="font-family: Arial; font-size: 15px; line-height: 15px; white-space: pre-wrap;">ANSWER: Sine and cosine have amplitudes of one because the Unit Circle's coordinates are at (0,1), (0,-1), (1,0), and (-1,0). If you look at (0,-1) and (0,1), these points are the graph's highest and lowest points on the graph. The amplitude is not going to pass one because that is where it reaches it's highest point, and it is at its lowest point at -1.</span><ul style="margin-bottom: 0pt; margin-top: 0pt;"><ul style="margin-bottom: 0pt; margin-top: 0pt;">
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Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-64473517757116794612014-03-20T00:55:00.004-07:002014-03-20T01:13:34.883-07:00BQ# 1: Unit P<span style="font-family: Georgia, Times New Roman, serif;">2. Law of Sines</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">SSA is ambiguous because we don't know if we will have no triangles, one triangle, or two triangles. We are only given one angle in this case. Now thinking back to the Unit Circle, we should remember how the lines on the circle are given to us by using Law of Sines when the radius is not equal to 1 as it has been given to us in Unit N.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">4. Area Formula</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">The base is b and h is the height of the triangle. Here are are not given the height, so we have to use arcsin of the angle which, in this case, is equal to h/a. We are using opposite over hypotenuse for whatever angle we are using; in this case, it is angle C. We then take sin of the angle times 1/2ab. However, sometimes it won't have a and b given, so we have to take what is given and make sure we haves its opposite angle. All the sides must be different, so just think of all the variables in the equation being different. Here are the other formulas we can use:</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">A= 1/2bcsinA</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">A=1/2acsinB</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">A=absinC</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Works Cited</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">http://www.compuhigh.com/demo/lesson07_files/oblique.gif</span>Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-5242140601292506042014-03-19T23:45:00.000-07:002014-03-19T23:45:14.753-07:00I/D3: Unit Q - Pythagorean Identities<div>
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<span style="font-family: Georgia, 'Times New Roman', serif; line-height: 17.25px; white-space: pre-wrap;"><b><span style="font-size: large;">Inquiry Activity Summary</span></b></span></div>
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<span style="font-family: Georgia, 'Times New Roman', serif; line-height: 17.25px; white-space: pre-wrap;">The Pythagorean is here again. We first saw it in unit N in the unit circle, and it relates to trig identities as well. Using x, y, and r, we can show that. (x^2/r^2)+(y^2/r^2)=(r^2/r^2) which is also (</span><span style="font-family: Georgia, 'Times New Roman', serif; line-height: 17.25px; white-space: pre-wrap;">x^2/r^2)+(y^2/r^2)=1. This can be simplified to </span><span style="font-family: Georgia, 'Times New Roman', serif; line-height: 17.25px; white-space: pre-wrap;">(</span><span style="font-family: Georgia, 'Times New Roman', serif; line-height: 17.25px; white-space: pre-wrap;">x/r)^2+(y/r)^2=1.</span><span style="font-family: Georgia, 'Times New Roman', serif; line-height: 17.25px; white-space: pre-wrap;"> sin2x+cos2x=1 comes from the unit circle. The ratio for cosine on the unit circle is x/r. The ratio for since is y/r. Here we are going to take one of the magic 3 ordered pairs: 30 degrees. cos30 is equal to radical 3 over 2 and sin30 is equal to 1/2. Radical 3 over 2 squared is equal to 3/4. 1/2 squared is equal to 1/4. 3/4+1/4=1 which is where you get the one on the right side. Since we squared these fractions, we have to show it in our identities also. This identity is actually the Pythagorean theorem moved around, hence it is also called the Pythagorean identity. Keep in mind that an identity is "a proven fact and formula that is always true." This tactic works with any degree from the magic 3.</span></div>
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<span style="font-family: Georgia, 'Times New Roman', serif; line-height: 17.25px; white-space: pre-wrap;">We can also derive the secant and tangent from sin2x+cos2x=1. If you divide all of that by cos2x, you will end up with tan2x+1=sec2x. With tanx=sinx/cosx, multiply the left and right sides by themselves to get a squared value for both. tanx*tanx=(sinx/cosx)(sinx/cos). In the end you will get tan2x=sin2x/cos2x.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif; font-size: large;"><span style="line-height: 18.399999618530273px; white-space: pre-wrap;"><b>Inquiry Activity Reflection</b></span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="vertical-align: baseline; white-space: pre-wrap;"><b><span style="color: #cc0000;">The connections that I see between Units N, O, P, and Q so far are</span></b> that they all relate to triangle and they all use the six trig functions.</span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="vertical-align: baseline; white-space: pre-wrap;"><b><span style="color: #cc0000;">If I had to describe trigonometry in THREE words, they would be</span></b> challenging, connected, and unexceptional.</span></span></div>
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Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-10181196880778999972014-03-18T00:50:00.003-07:002014-03-24T21:11:00.040-07:00WPP#13-14: Unit P Concept 6 & 7 - Law of Sines/Cosines<span style="background-color: white;"><span style="color: #38761d;"><span style="font-family: Georgia, Utopia, 'Palatino Linotype', Palatino, serif; font-size: 14px; line-height: 21.735000610351563px;">This WPP 13-14 was made in collaboration with Tracey Pham. Please visit the other awesome posts on her blog by going <a href="http://traceypperiod5.blogspot.com/2014/03/wpp13-14-unit-p-concept-6-7-law-of.html" target="_blank">HERE</a>.</span></span></span>Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-55940755032629788432014-03-06T23:40:00.003-08:002014-03-06T23:57:18.853-08:00WPP #12 Unit O Concept 10: Angle of Depression and Elevation<span style="font-family: Georgia, Times New Roman, serif; font-size: large;">Elevation</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">Yoshi is filming his music video and wants to have his
shot at the beach. For one of his shots, he is going to be standing at the top
of a lighthouse while the camera will be on the floor 18 feet away from the
lighthouse. The angle of elevation from the camera lense to the top of the lighthouse is 34*14'. What is the height of the lighthouse?</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Answer: 12.25 m</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Elevation</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Depression</span></div>
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<span style="font-family: Georgia, 'Times New Roman', serif; text-align: center;">Yoshi is now on the other side of the lighthouse. He hears his fans cheering him on from below 36.8 m away and looks straight at them and waves. What is the angle of depression if he was standing on the same leveled lighthouse? (Hint: disregard the orange-ish lines labeling 12.25 m; the lighthouse from Yoshi to the floor is 12.25)</span></div>
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<span style="font-family: Georgia, 'Times New Roman', serif; text-align: center;">Answer: 34.24*</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Depression</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">SHOW YOUR WORK</span><br />
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Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-5581084768224590752014-03-04T22:59:00.004-08:002014-03-04T23:09:44.345-08:00I/D2: Unit O - Derive the SRTs<span style="background-color: purple; font-size: 13px; font-weight: bold;"><span style="color: white; font-family: Georgia, Times New Roman, serif;">INQUIRY ACTIVITY SUMMARY</span></span><br />
<span style="color: #666666; font-family: Georgia, Times New Roman, serif; font-size: x-small;"><span style="background-color: #f2f2f2;">As seen in the square, you have to cut it diagonally because that is how you can get two triangles. If they are equally bisected, they will form two 45-45-90 triangles. You get the hypotenuse by using the Pythagorean theorem (a^2+b^2=c^2). We are told that the side lengths of the square are 1. That means the side lengths of a and b of the triangle are 1 as well. You take (1)^2+(1)^2=c^2. That will give you c=radical 2; this is your hypotenuse. "n" means the variable used to find your sides. Since in a 45-45-90 degree triangle the sides corresponding to the 45 degree angles are the same, we can label them with "n." </span></span><br />
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<a href="http://1.bp.blogspot.com/-BDG0_HSZOjk/UxbNAwZO2qI/AAAAAAAAAKk/U8s9TXbYFqs/s1600/454590+work.jpg" imageanchor="1" style="background-color: white; font-family: Georgia, 'Times New Roman', serif; font-size: 13px; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://1.bp.blogspot.com/-BDG0_HSZOjk/UxbNAwZO2qI/AAAAAAAAAKk/U8s9TXbYFqs/s1600/454590+work.jpg" height="240" width="320" /></a><br />
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<span style="background-color: #f2f2f2; color: #666666;"><span style="font-family: Georgia, Times New Roman, serif; font-size: x-small;">In the 30-60-90 triangle, I got it by bisecting an equilateral triangle down the center. Since the sides of the equilateral are equal to 1, I knew the hypotenuse was 1. The base is 1/2 since we cut the triangle in half. I then used Pythagorean theorem to find the height which gave me a=radical 3 over 2. This translates to the normal pattern because side a is n equal to n. The hypotenuse is double that. Here we see that side a (1/2) was multiplied by 2. (2)(1/2)=1; that is our hypotenuse. To find the height, we are most familiar with n radical 3. Our n in 1/2. We multiply that by radical 3. That gives us radical 3 over 2 as our height. We use n because that's the variable we are most familiar with when we first learned about triangles in geometry. In this problem the b is n, the hypotenuse is 2n and the height is n radical 3.</span></span><br />
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<span style="background-color: purple; font-size: 13px;"><b><span style="color: white; font-family: Georgia, Times New Roman, serif;">INQUIRY ACTIVITY REFLECTION</span></b></span><br />
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<span style="background-color: #f2f2f2;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Something I never noticed before about special right triangles is</span></b></span><br />
<span style="background-color: #f2f2f2; color: #666666; font-size: 13px;"><span style="font-family: Georgia, Times New Roman, serif;">that they can be made from squares and triangles. After learning the unit circle, I thought special triangles were only used in that.</span></span><br />
<span style="background-color: white;"><b><span style="color: #741b47; font-family: Georgia, Times New Roman, serif;">Being able to derive these patterns myself aids in my learning because</span></b></span><br />
<span style="background-color: white; color: #666666; font-size: 13px;"><span style="font-family: Georgia, Times New Roman, serif;">I now better understand my last unit as well as understand where my values come from. Before I just had to memorize the values of each side without knowing how I got them.</span></span><br />
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Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-20222493442890131742014-02-22T11:27:00.001-08:002014-02-22T11:43:36.133-08:00I/D1: Unit N - How do SRT and UC relate?<span style="background-color: white; font-family: arial, sans-serif; font-size: 13px; font-weight: bold;">INQUIRY ACTIVITY SUMMARY</span><br />
<span style="font-family: Arial; font-size: 15px; line-height: 1.15; white-space: pre-wrap;">Describe the 30* triangle</span><br />
<span style="font-family: Arial; font-size: 15px; line-height: 1.15; white-space: pre-wrap;"> Click HERE.</span>
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<span style="font-family: Arial; font-size: 15px; line-height: 1.15; white-space: pre-wrap;">Describe the 45* triangle</span><br />
<span style="font-family: Arial; font-size: 15px; white-space: pre-wrap;">Click HERE.</span>
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<span style="font-family: Arial; font-size: 15px; white-space: pre-wrap;">Describe the 60* triangle</span><br />
<span style="font-family: Arial; font-size: 15px; white-space: pre-wrap;">Click HERE.</span><br />
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<b><span style="color: #274e13; font-size: large;"><span style="font-family: arial, sans-serif;"><span style="background-color: white;">1. </span></span><span style="font-family: Arial; line-height: 1.15; white-space: pre-wrap;">The coolest thing I learned from this activity was...</span></span></b><br />
<span style="font-family: Arial;"><span style="font-size: 15px; line-height: 17.25px; white-space: pre-wrap;">how to find these points and coordinates mathematically instead of memorizing it by heart.</span></span><br />
<span style="font-family: Arial; line-height: 1.15; white-space: pre-wrap;"><b><span style="color: #274e13; font-size: large;">2. This activity will help me in this unit because...</span></b></span><br />
<span style="font-family: Arial; font-size: 15px; line-height: 1.15; white-space: pre-wrap;">I can now better understand how to label my triangles and my unit circle. It also showed me patterns I didn't notice before.</span><br />
<span style="font-family: Arial; white-space: pre-wrap;"><span style="color: #274e13; font-size: large;"><b><span style="line-height: 17.25px;">3. </span>Something I never realized before about special right triangles and the unit circle is…</b></span></span><br />
<span style="font-family: Arial; font-size: 15px; white-space: pre-wrap;">that they actually relate to each other! I was told that in past math courses, but I didn't quite grasp what it meant.</span>Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-87677651259349124852014-02-10T21:20:00.001-08:002014-02-10T21:22:44.389-08:00RWA#1: Unit M Concept 5: Graphing Ellipses Given an Equation and Identifying All Parts<span style="font-family: Georgia, Times New Roman, serif;">1. The mathematical definition of an <b>ellipse</b> is <span style="background-color: #8e7cc3; color: white;">"the set of all points such that the sum of the distance from two points is a constant." </span></span><span style="font-family: Georgia, Times New Roman, serif;">(</span><span style="font-family: Georgia, Times New Roman, serif;">http://www.mhhe.com/math/precalc/barnettca2/student/olc/graphics/barnett01caaga_s/ch07/downloads/pc/ch07section2.pdf)</span><br />
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<a href="http://img.sparknotes.com/content/testprep/bookimgs/sat2/math2c/0006/ellipse.gif" imageanchor="1" style="background-color: white; margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" src="http://img.sparknotes.com/content/testprep/bookimgs/sat2/math2c/0006/ellipse.gif" /></span></a></div>
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<span style="font-family: Georgia, Times New Roman, serif;">2. An ellipse is <i>algebraically</i> shown with the equation written in standard form:<span style="background-color: white; line-height: 18.479999542236328px;"> </span><span style="background-color: #8e7cc3; line-height: 18.479999542236328px;"><span style="color: white;">(x-h)^2/a^2+(y-k)^2/b^2=1 or (x-h)^2/b^2+(y-k)^2/a^2.</span></span></span><span style="background-color: white; line-height: 18.479999542236328px;"><span style="font-family: Georgia, Times New Roman, serif;"> The center is always (h,k). "a" is always bigger than "b." Remember that a and b are squared in the equation, so you have to take the square root of them when writing them out on the template.</span></span><br />
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<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">It can be <i>graphically</i> shown as a </span><span style="background-color: #8e7cc3; color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">visual on a graph</span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">. An ellipse typically looks like a squished circle from its sides or top and bottom.</span><br />
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<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;"><u>Here is how you can identify key parts on the graph:</u></span><br />
<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">If a is under x in the equation (the first one listed above), the graph will be fat. </span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">The major axis length is 2a (Mrs. Kirch shows this with a solid line); the minor axis length is 2b (she shows this with a dotted line). In this kind of equation, the major axis will run horizontally.</span><br />
<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">To find vertices: Count "a" units from the center going left and right; plot these points. To find co-vertices: </span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">Count "b" units from the center going up and down; plot these points.</span><br />
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<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">If a is under y in the equation (the second one listed above), the graph will be skinny. </span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">The major axis length is 2a; the minor axis length is 2b. In this kind of equation, the major axis will run vertically. To find vertices: </span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">Count "a" units from the center going up and down; plot these points. To find co-vertices: </span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">Count "b" units from the center going left and right; plot these points.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="background-color: white; line-height: 18.479999542236328px;">The foci effects the shape because the further away it is to the vertices, the more it will have to "focus" on that point. When the foci increases, the eccentricity does, too. To find your foci, the major axis value will be the number that does NOT change in the foci points. (ex. If the major axis is y=-2, your two foci will be (#, -2).) To find the other number, (ex. It would be x.), you take the value from your minor axis and add AND subtract it to/from your c value. </span></span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">In order to find c, you use the equation a^2+b^2=c^2.</span><br />
<span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">Your eccentricity is greater than 0 but less than 1 and can be found with "c/a.</span><br />
<span style="font-family: Georgia, Times New Roman, serif;"><span style="background-color: white; line-height: 18.479999542236328px;"><br /></span><span style="background-color: white; line-height: 18.479999542236328px;">Do you want to see a problem worked out? Watch this video example.</span></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">3. A real world application of an ellipse would be <span style="background-color: #8e7cc3;"><span style="color: white;">when you tilt your glass cup with a drink to take a sip out of it</span></span>. The drink in your cup will form an ellipse around the cup's interior. </span><span style="font-family: Georgia, 'Times New Roman', serif;">Let's take for example a glass of milk. When the milk is in the cup and set on the table, you may notice the top of the milk is shaped as a circle. Once you begin to tilt the cup and bring it to your mouth for a sip, the shape at the top of the milk is no longer a circle.</span><br />
<a href="http://cdn.c.photoshelter.com/img-get/I0000RM3hrmrL0Po/s/750/750/usn2043-Glass-of-Milk.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://cdn.c.photoshelter.com/img-get/I0000RM3hrmrL0Po/s/750/750/usn2043-Glass-of-Milk.jpg" height="250" width="320" /></a><br />
<span style="font-family: Georgia, 'Times New Roman', serif;">The ellipse is formed because the eccentricity has increased. It will continue to increase as you tilt the cup. The center of the ellipse moves further from the center of the cup the more you title your cup. I would associate this example as a skinny ellipse represented with the equatio<span style="background-color: white;">n </span></span><span style="background-color: white; font-family: Georgia, 'Times New Roman', serif; line-height: 18.479999542236328px;">(x-h)^2/b^2+(y-k)^2/a^2 because the cup's ellipse would be facing me. The point closest to my lip and furthest to me would be the vertices. The left and right side of the cup would be my co-vertices.</span><br />
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<span style="background-color: white; color: #333333; line-height: 18.200000762939453px;"><span style="font-family: Georgia, Times New Roman, serif;">4. Works Cited</span></span><br />
<span style="font-family: Georgia, Times New Roman, serif;"><span style="background-color: white; color: #333333; line-height: 18.200000762939453px;">Ellipse Image pasted from: </span><span style="color: #333333;"><span style="line-height: 18.200000762939453px;"><a href="http://img.sparknotes.com/content/testprep/bookimgs/sat2/math2c/0006/ellipse.gif">http://img.sparknotes.com/content/testprep/bookimgs/sat2/math2c/0006/ellipse.gif</a></span></span><br style="background-color: white; color: #333333; line-height: 18.200000762939453px;" /><span style="background-color: white; color: #333333; line-height: 18.200000762939453px;">Tilted Milk Cup Image pasted from: </span><span style="color: #333333;"><span style="line-height: 18.200000762939453px;"><a href="http://lisamasson.photoshelter.com/image/I0000RM3hrmrL0Po">http://lisamasson.photoshelter.com/image/I0000RM3hrmrL0Po</a></span></span><br style="background-color: white; color: #333333; line-height: 18.200000762939453px;" /><span style="background-color: white; color: #333333; line-height: 18.200000762939453px;">Ellipse Video Example video from: </span><a href="http://www.youtube.com/watch?v=wTGA9D4Y0qk">http://www.youtube.com/watch?v=wTGA9D4Y0qk</a></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Ellipse website link pasted from: <u><a href="http://www.mhhe.com/math/precalc/barnettca2/student/olc/graphics/barnett01caaga_s/ch07/downloads/pc/ch07section2.pdf">http://www.mhhe.com/math/precalc/barnettca2/student/olc/graphics/barnett01caaga_s/ch07/downloads/pc/ch07section2.pdf</a></u></span></div>
Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-17756904036848953422013-12-30T19:21:00.001-08:002013-12-30T19:22:50.250-08:00WPP#10: Unit L Concept 9-14 - Basic probability(one event), probability of independent "AND" events(multiple events with and without replacement), probability of "OR" events(mutually and non-mutually exclusive), and probability of events that require Combinations to determine sample space<iframe frameborder="0" marginheight="0" scrolling="no" src="http://www.mentormob.com//learn/widget/314914/580/99cc33/3-0" style="-moz-border-radius: 10px; -webkit-border-radius: 10px; background: #99cc33; border-radius: 10px; height: 248px; overflow: hidden; width: 580px;"></iframe><br />
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Step 4 and Step 5 are switched.</div>
Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-84768151166539997482013-12-18T00:20:00.001-08:002013-12-18T00:20:50.460-08:00WPP#9: Unit L Concept 4-8 - Calculating possibilities with FCP, combinations(one event and multiple events), permutations, and distinguishable permutations <iframe frameborder="0" marginheight="0" scrolling="no" src="http://www.mentormob.com//learn/widget/312449/580/99cc33/3-0" style="-moz-border-radius: 10px; -webkit-border-radius: 10px; background: #99cc33; border-radius: 10px; height: 248px; overflow: hidden; width: 580px;"></iframe><br />
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Create your own Playlist on <a href="http://www.mentormob.com/">MentorMob!</a></div>
Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-60394592585246299152013-12-08T15:50:00.003-08:002013-12-08T16:14:35.189-08:00SP#6: Unit K Concept 10 - Find Sums of Infinite Geometric Series<img src="webkit-fake-url://200E25F4-8049-4626-B624-8846E78DA71A/imagejpeg" /><br />
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Make sure you pay close attention to what numbers to plug into each part of the formula. I tried my best to color code it, so it is easier to follow along. Also, don't forget about that whole number! Adding it to the last part of your problem is what gives you your final answer.</div>
Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-10931052904641410262013-12-01T23:45:00.002-08:002013-12-01T23:54:00.981-08:00Fibonacci Beauty Ratio (Extra Credit)<span style="background-color: white;"><span style="color: #cc0000;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Stephanie V.</span><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"> </span></span></span><br />
<span style="background-color: white;"><span style="color: #cc0000;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Foot to Navel: 99 cm Navel to top of Head: 63 cm Ratio: 99/63=1.571 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Navel to chin: 45 cm chin to top of head: 23 cm Ratio:45/23=1.957 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Knee to navel: 53 cm Foot to knee: 52 cm Ratio: 53/52=1.019 cm </span></span></span><br />
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<span style="background-color: white;"><span style="color: #cc0000;">Average: 1.516 cm</span></span></div>
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<span style="background-color: white;"><span style="color: #a64d79;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Helena C.</span><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"> </span></span></span><br />
<span style="background-color: white;"><span style="color: #a64d79;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Foot to Navel: 102 cm Navel to top of Head: 66 cm Ratio: 102/66=1.545 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Navel to chin: 45 cm chin to top of head: 22 cm Ratio:45/22=2.045 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Knee to navel: 56 cm Foot to knee: 45 cm Ratio: 56/45=1.244 cm </span></span></span><br />
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<span style="background-color: white;"><span style="color: #a64d79;">Average: 1.611 cm</span></span></div>
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<span style="background-color: white;"><span style="color: #f1c232;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Joshua N.</span><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"> </span></span></span><br />
<span style="background-color: white;"><span style="color: #f1c232;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Foot to Navel: 102 cm Navel to top of Head: 67 cm Ratio: 102/67.=1.522 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Navel to chin: 45 cm chin to top of head: 23 cm Ratio: 45/23= 1.957 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Knee to navel: 61 cm Foot to knee: 47 cm Ratio: 61/47=1.300 cm </span></span></span><br />
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<span style="background-color: white;"><span style="color: #f1c232;">Average: 1.629 cm</span></span></div>
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<span style="background-color: white;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"><span style="color: #6aa84f;">Rodolfo R. </span></span></span><br />
<span style="background-color: white;"><span style="color: #6aa84f;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Foot to Navel: 100 cm Navel to top of Head: 64 cm Ratio: 100/64 =1.563 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Navel to chin: 46 cm chin to top of head: 25 cm Ratio:46/25= 1.840 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Knee to navel: 54 cm Foot to knee: 46 cm Ratio: 54/46=1.174 cm </span></span></span><br />
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<span style="background-color: white;"><span style="color: #6aa84f;">Average: 1.526 cm</span></span></div>
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<span style="background-color: white;"><span style="color: #3d85c6;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Christine N.</span><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;"> </span></span></span><br />
<span style="background-color: white;"><span style="color: #3d85c6;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Foot to Navel: 96 cm Navel to top of Head: 60 cm Ratio: 96/60= 1.6 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Navel to chin: 42 cm chin to top of head: 22 cm Ratio: 42/22= 1.909 cm </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 18px;">Knee to navel: 51 cm Foot to knee: 45 cm Ratio: 51/45= 1.133 cm </span></span></span><br />
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<span style="background-color: white;"><span style="color: #3d85c6;">Average: 1.547 cm</span></span><br />
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<span style="background-color: white; color: #e69138;">According to Fibonacci's Beauty Ratio test, Helena C was the most beautiful person I measured. Her measurements were but 0.007 away from the Golden Ratio. Her ratios included: 1.545, 2.045, and 1.244 cm which averaged to 1.611. I believe the Beauty Ratio is a huge disclaimer because the friends I measured besides Helena were beauty to me as well. Yes, Josh and Rodolfo, too! However, it did show how proportional parts of our body can be, and that is what makes it stand out to others. True beauty comes from within; some show their beauty more than others. But as I've said before in my haiku, <i>we are all ugly</i>.</span></div>
Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-13238010017001179932013-11-24T18:55:00.000-08:002013-11-29T18:57:16.899-08:00Fibonacci Haiku: We Are All Ugly<br />
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<span style="font-family: Georgia, Times New Roman, serif;">Fibonacci</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">1.618</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Golden ratio</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Add current previous</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Snails are prettier than me</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Thanks to Mr. Fib we are all ugly</span></div>
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Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-63161855892315761882013-11-15T13:45:00.001-08:002013-11-15T13:46:36.853-08:00SP#5: Unit J Concept 6 - Partial Fraction Decomposition with Repeated Factors<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-wfoaUREzKPw/UoaVW33-hdI/AAAAAAAAAIY/TDU1lBfT_c4/s1600/P1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="http://1.bp.blogspot.com/-wfoaUREzKPw/UoaVW33-hdI/AAAAAAAAAIY/TDU1lBfT_c4/s400/P1.jpg" width="400" /></a></div>
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When decomposing these problems, make sure you count up the powers. If there is an (x-2)^2, make sure you give one factor and (x-2) denominator then the one next to it should have an (x-2)^2 denominator. Also, When you check your answer on a calculator, it should be in Row-Echelon Form. The numerators of the decomposed answer comes directly from what the calculator reads.</div>
<br />Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-76538071295006032902013-11-15T13:40:00.002-08:002013-11-15T13:46:27.404-08:00SP#4: Unit J Concept 5 - Partial Fraction Decomposition with Distinct Factors<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-0A1HywIZqBs/UoaUkbuQkBI/AAAAAAAAAIM/o5R1kyV_BWw/s1600/2013-11-15+13.33.19.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="300" src="http://4.bp.blogspot.com/-0A1HywIZqBs/UoaUkbuQkBI/AAAAAAAAAIM/o5R1kyV_BWw/s400/2013-11-15+13.33.19.jpg" width="400" /></a></div>
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Be sure to combine your like terms correctly. Don't forget the A, B, or C in front of each variable. Also, make sure you distribute the common denominator to the top as well. Without it, your like terms will be completely wrong.</div>
<br />Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-2850146558391133462013-11-14T22:24:00.001-08:002013-11-14T22:35:40.792-08:00SV#5 Unit J Concept 3-4 - Solving for MatricesClick <a href="http://www.educreations.com/lesson/view/sv5/13611676/?s=6dDuqi&ref=app" target="_blank">HERE</a> to watch my video.<a href="http://http//www.educreations.com/lesson/view/sv5/13611676/?s=6dDuqi&ref=app"></a><br />
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Solving for matrices can be super tricky! Just make sure not to confuse your z's with a 2. That tends to throw many people off. Also, make sure your elementary row operations are correct. This is the easiest part of solving for matrices, but one little mistake will ruin your entire answer.Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-14213052605074433272013-11-11T22:29:00.000-08:002013-11-12T13:37:56.292-08:00WPP #6: Unit I Concept 3-5 - Compound Interest & Investment Application Problems<iframe frameborder="0" marginheight="0" scrolling="no" src="http://www.mentormob.com//learn/widget/300686/580/99cc33/3-0" style="-moz-border-radius: 10px; -webkit-border-radius: 10px; background: #99cc33; border-radius: 10px; height: 248px; overflow: hidden; width: 580px;"></iframe><br />
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Missing last step<br />
<img alt="image.jpeg" class="hv" height="300" src="https://mail.google.com/mail/u/0/?ui=2&ik=76d665bb70&view=att&th=1424af5548d4e042&attid=0.0&disp=thd&zw" width="400" /></div>
Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-31573751300933493292013-11-11T20:47:00.001-08:002013-11-11T20:51:56.182-08:00SV#4: Unit I Concept 2 - Graphing Logarithmic Functions and Identifying Key Parts<div style="text-align: center;">
To watch my video, click <a href="http://www.educreations.com/lesson/view/sv3/13381150/?s=qUaYhU&ref=app" style="font-family: Cantarell; font-size: small; line-height: 18px;" target="_blank">HERE</a>.</div>
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<span style="font-family: Cantarell;"><span style="line-height: 18px;">In this vid</span></span><span style="font-family: Cantarell; line-height: 18px;">eo, you should be aware of the order that I solved my key parts in. I skipped key points because I felt like it would be more relevant once I start graphing the equation. Also, make sure that you plug in the zeros into the correct number for finding x and y intercepts. Remember that finding x-intercepts require you to plug in zero to the variable "y." For y-intercepts, you plug the zero into the variable "x."</span><br />
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<span style="font-family: Cantarell; font-size: x-small; font-weight: normal; line-height: 18px;"><i>P.S. I apologize for sounding like a dying cat. I had to pause the video a few times to clear my throat. Sorry if the abrupt changes in volumes and tones scared you.</i></span></div>
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Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0tag:blogger.com,1999:blog-4636673114301680768.post-63857800824465249862013-10-25T13:52:00.000-07:002013-11-12T13:33:39.998-08:00SP#3: Unit I Concept 1 - Graphing Exponential Functions and Identifying Key Parts<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-oMm6wiJ8Kf0/UoKepWpZBHI/AAAAAAAAAG4/LGlLUzI2e38/s1600/2013-11-12+13.30.11.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://1.bp.blogspot.com/-oMm6wiJ8Kf0/UoKepWpZBHI/AAAAAAAAAG4/LGlLUzI2e38/s320/2013-11-12+13.30.11.jpg" width="320" /></a></div>
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<a href="http://2.bp.blogspot.com/--oCmxIGsv4E/UoKepaCmZ9I/AAAAAAAAAHA/oSPipMAT71A/s1600/2013-11-12+13.30.26.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://2.bp.blogspot.com/--oCmxIGsv4E/UoKepaCmZ9I/AAAAAAAAAHA/oSPipMAT71A/s320/2013-11-12+13.30.26.jpg" width="320" /></a></div>
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<img src="webkit-fake-url://F0D052CF-2326-40D1-8F03-C78341B1C8B4/imagejpeg" /><img src="webkit-fake-url://C0363A59-D548-4F30-86D7-B6B10FA865C3/imagejpeg" />Be sure to carefully plug the graph into the calculator to find your key points. Also, be sure that you write your range correctly. Negative infinity always goes before your asymptote.<img src="webkit-fake-url://8A176CD7-B50B-4238-811D-1612B61EC85D/imagejpeg" />Diana P.http://www.blogger.com/profile/16432125832118264467noreply@blogger.com0