Question

A window in Prof. Purugganan's office: every morning, before he leaves her office, prof. Purugganan draws the curtain over the window. Every morning she draws the curtain open, starting at time t = 0. If he draws the curtain at the rate of 0.8 ft/ sec, find the rate at which the area of the exposed part of the window's glass is changing when t = 4. f is given by f(s) = 5 sin (pi/32(s^2+16)).

Answer 1

Wow. What is f(s) supposed to represent? What's s?

Answer 2

Do you mean\[f(s) =\sin \frac{ \pi }{ 32(s^2+16)}?\]

Answer 3

f(s) is supposed to represent the shape of the curtain

Answer 4

If not, change your formula accordingly.

Answer 5

Wow again. What a complicated curtain! My curtains are bed sheets.

Answer 6

\[5 \sin ((\pi/32)(s^2+16))\] sorry, this is what it is supposed to look like

Answer 7

thanks for the clarification. Much better. Suppose that f(s) represents the area in question. You'll need to differentiate your expression with respect to s. I'd much rather that this problem involved t instead of s, since t usually represents time.

Answer 8

Finding the derivative with respect to s supposedly gives us a formula for the time rate of change of the exposed area of the window.

Answer 9

Technically it is f(t); my professor uses f(s) instead of f(t) (what I was taught in hs) and it is confusing

Answer 10

Can you find this derivative?
Once you've found it, set time = s = 4 sec and calculate the rate of change of area of the window at that time.

surely is confusing. Teacher probably wants to help you learn to cope with non-standard situations.

Answer 11

f'(s) = \[-5/16\pi s \sin(\pi s^2/32)\]

Answer 12

the pi and s should be above the 16. formatting is wrong. same with pi s^2

Answer 13

so i find f'(s)? I thought I had to use integration for this problem

Answer 14

The derivative must also have (s^2+16) as part of the input.

if y = sin x, dy/dx = cos x, right?

If y = sin (s^2+16), dy/ds = cos (s^2+16) [2s]

Answer 15

You're finding a rate of change; therefore, use differentiation.

Answer 16

Once again, I'm verifying that I understand what you've shared:

Answer 17

\[f(s)=\sin[\frac{ \pi }{ 32 }(s^2+16)]\]

Answer 18

on target or not?

Answer 19

there is a 5 in front of the sin, otherwise everything is correct

Answer 20

If you accept this, find the derivative f ' (s).

Answer 21

Fine. Then, the derivative would start out with

f '(s) = 5 something

Answer 22

f ' (s) = 5 cos [ ] * (d/ds) [ ]

Answer 23

... where the [ ] part can be found above.