Question

I need help:( Finals tomorrow!!

A weight is attached to a spring that I fixed to the floor. The equation h=7cos(pi/3t)models the height, h, in centimeters after t seconds of the weight being stretched and released.
a.Solve the equation for t
b.Find the times at which is the first at a height of 1cm, of 3cm and of 5cm above the rest position. Round your answer to the nearest hundredth.
c.Find the times at which the weigth is at a height of 1cm, 3cm and 5cm below the rest position for the second time. Round your answers to the nearest hundredth.

Please help I'm overwhelmed:(

Answer 1

@AravindG Can you help?

Answer 2

@whpalmer4 Can you help? Haha anyone?

Answer 3

Yes, I think I can help.

\[h = 7\cos(\frac{\pi}{3}t)\]How would you solve that for \(t\)?

Answer 4

Give me a sec i need to do this on paper!

Answer 5

I got t=arc cos (h/7)/pi

Answer 6

I'd divide both sides by 7, then take the arc cos of each side. Multiply both sides by 3/pi and you're done...

Answer 7

you lost a 3 in there somewhere...

Answer 8

t=3arc cos (h/7)/pi

Answer 9

but you had the right general idea, clearly. good.

okay, now you need to use your shiny new formula to find the value of t when h = 1 cm, 3 cm, 5 cm

Answer 10

So do I solve the problem three separate times but starting with 1cm first? Just sub it in for h?

Answer 11

So when I plugged in 1cm for h and solved I got

t=0.4544

Answer 12

Yes, you just evaluate
\[t = \frac{3}{\pi}\cos^{-1}(\frac{h}{7})\] for the 3 different values of \(h\)

Answer 13

hmm, that's not what I get, are you sure you are working in radians?

Answer 14

Hold on let me try again

Answer 15

If I plug that value of \(t\) into the formula, I get 6.22234

Answer 16

When I did it that way I got 12.3718

Answer 17

Okay,let's try this 1 step at a time. Punch in 1/7, what do you get?

Answer 18

8.1851?

Answer 19

Press the clear button — 1/7 = 0.142857142857142857...

Answer 20

Ohhh. Sorry haha ok i got that

Answer 21

now take the arc cosine of that...

Answer 22

Wait how would i set that up?

Answer 23

What kind of a calculator do you have?

Answer 24

Some online calculator my school provides. Dream calc?

Answer 25

hmm. well, hard to know for sure, but how about doing the 1/7 calculation, then with the result still on the screen, press the Shift button and the cos button and report what you get

Answer 26

0.9898

Answer 27

Oh, you didn't press the shift button - that's the result you would get for just cosine of 1/7

Answer 28

So for 2 its 0.9595

Answer 29

Sorry I dont do 2 i mean 3
3=0.9096

Answer 30

No, let's go back to what we were trying to do with the step by step calculation.

1/7
press shift, then cos
what do you get?

Answer 31

Well, you're apparently having issues operating the calculator correctly. Frustrating for both of us!

We need to evaluate \[t = \frac{3}{\pi}\cos^{-1}(\frac{h}{7})\]for \(h=1,3,5\)

\[t=\frac{3}{\pi}\cos^{-1}(\frac{1}{7}) = \frac{3}{3.14159}\cos^{-1}{0.142857} \approx 1.363\]
\[t=\frac{3}{\pi}\cos^{-1}(\frac{3}{7}) = \frac{3}{3.14159}\cos^{-1}{0.428571} \approx 1.077\]
\[t=\frac{3}{\pi}\cos^{-1}(\frac{5}{7}) = \frac{3}{3.14159}\cos^{-1}{0.714285} \approx 0.74\]

Answer 32

Note that I have not done the specified rounding.

For the third part, you want to do the same procedure, except this time your h values will be -1, -3, -5.

Good luck on the final!