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1.
Content!
2.
Question 1.
3.
• We start by listing all of the given information
4.
• We divide diameter by 2 to get the radius • Notice that the units for are different for each piece of information (feet and inches) •
We divide the number of inches by 12 to convert the radius into units of feet
5.
• Now with all of our variables listed, we find the relationship between them according to that of a sphere
6.
• Next we differentiate implicitly with respect to time followed by inputting the given information
7.
• Solve for dr/dt and complete with a sentence answer • Include units of measure
8.
*Side note: Some general volume equations for solids that should be known
9.
Question 2.
10.
• We start again by listing the information given
11.
• Find the relationship between the variables. In this case, it is the circumference formula
12.
• Now we differentiate implicitly with chain rule with respect to time and input the variables listed • Solve for dC/dt
13.
• Finish with a sentence answer and include appropriate units of measure
14.
Question 3.
15.
• Start by drawing out a diagram and listing all given information
16.
• Note that the two triangles are similar and therefore, we can find an expression for ds/dt using the idea of proportionality • Solve for ds/dt, the rate at which the shadow is increasing in length
17.
• Now, with an expression relating the distances x and s, we differentiate implicitly with respect to time and solve for the rate at which the tip of the shadow is moving
18.
Bonus Question! Just some extra practice =)
19.
• List all given information • Note that to find the distance travelled at 1 minute, multiply the rate by time (in seconds) •
Now, find the relationship between the distances
20.
• Next we differentiate implicitly using chain rule with respect to time and solve for dd/dt, the rate at which the distance between the girls is increasing
21.
• Finish with a sentence answer and include the appropriate units! =)
22.
DONEDONEDONE! =)
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