007A Sample Midterm 2, Problem 5 - Revision history

Kayla Murray at 04:01, 12 November 2017

2017-11-12T04:01:59Z

Kayla Murray at 13:25, 3 November 2017

2017-11-03T13:25:21Z

Kayla Murray at 00:35, 3 November 2017

2017-11-03T00:35:30Z

Kayla Murray: Created page with " A kite 30 (meters) above the ground moves horizontally at a speed of 6 (m/s). At what rate is the length of the string increasing when 50 (meters) of the s..."

2017-11-03T00:24:20Z

Created page with "<span class="exam"> A kite 30 (meters) above the ground moves horizontally at a speed of 6 (m/s). At what rate is the length of the string increasing when 50 (meters) of the s..."

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<span class="exam"> A kite 30 (meters) above the ground moves horizontally at a speed of 6 (m/s). At what rate is the length of the string increasing when 50 (meters) of the string has been let out?

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Foundations:  
|-
|'''The Pythagorean Theorem'''
|-
|        For a right triangle with side lengths  <math style="vertical-align: -4px">a,b,c</math>  where  <math style="vertical-align: 0px">c</math>  is the length of the
|-
|
        hypotenuse, we have  <math style="vertical-align: -2px">a^2+b^2=c^2.</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Exam Solution:  
|-
|[[File:9AF_5_GP.png|center|550px]]
|-
|<math style="vertical-align: -3px">30^2+h^2=s^2</math>
|-
|<math style="vertical-align: -4px">s=50</math>
|-
|
<math>\begin{array}{rcl}
\displaystyle{h} & = & \displaystyle{\sqrt{s^2-30^2}}\\
&&\\
& = & \displaystyle{\sqrt{50^2-30^2}}\\
&&\\
& = & \displaystyle{40}
\end{array}</math>
|-
|<math>2hh'=2ss'</math>
|-
|<math>2(40)6=2(50)s'</math>
|-
|<math>\begin{array}{rcl}
\displaystyle{s'} & = & \displaystyle{\frac{2(40)(6)}{2(50)}}\\
&&\\
& = & \displaystyle{\frac{24}{5} \text{ m/s}}
\end{array}</math>
|}

'''Detailed Solution:'''

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 1:  
|-
|[[File:9AF_5_GP.png|center|550px]]
|-
|From the diagram, we have  <math style="vertical-align: -3px">30^2+h^2=s^2</math>  by the Pythagorean Theorem.
|-
|Taking derivatives, we get
|-
|
        <math>2hh'=2ss'.</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 2:  
|-
|If   <math style="vertical-align: -4px">s=50,</math>  then
|-
|       <math style="vertical-align: -2px">h=\sqrt{50^2-30^2}=40.</math>
|-
|So, we have
|-
|        <math style="vertical-align: -5px">2(40)6=2(50)s'.</math>
|-
|Solving for   <math style="vertical-align: -5px">s',</math>  we get   <math style="vertical-align: -14px">s'=\frac{24}{5} \text{ m/s.}</math>  
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Final Answer:  
|-
|       <math style="vertical-align: -14px">s'=\frac{24}{5} \text{ m/s}</math> 
|}
[[007A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

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 <hr>
-(insert picture of handwritten solution)
+[[007A Sample Midterm 2, Problem 5 Solution|'''<u>Solution</u>''']]
 [[007A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

@@ Line 1: / Line 1: @@
 <span class="exam"> A kite 30 (meters) above the ground moves horizontally at a speed of 6 (m/s). At what rate is the length of the string increasing when 50 (meters) of the string has been let out?
 <hr>
-'''Detailed Solution'''
+[[007A Sample Midterm 2, Problem 5 Detailed Solution|'''<u>Detailed Solution for this Problem</u>''']]
 [[007A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

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 <span class="exam"> A kite 30 (meters) above the ground moves horizontally at a speed of 6 (m/s). At what rate is the length of the string increasing when 50 (meters) of the string has been let out?
+<hr>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Foundations: &nbsp;
+!Solution: &nbsp;
 |-
 |[[File:9AF_5_GP.png|center|550px]]
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-'''Detailed Solution:'''
+'''Detailed Solution'''
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"