anonymous
  • anonymous
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:(
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@AravindG Can you help?
anonymous
  • anonymous
@whpalmer4 Can you help? Haha anyone?
whpalmer4
  • whpalmer4
Yes, I think I can help. \[h = 7\cos(\frac{\pi}{3}t)\]How would you solve that for \(t\)?

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anonymous
  • anonymous
Give me a sec i need to do this on paper!
anonymous
  • anonymous
I got t=arc cos (h/7)/pi
whpalmer4
  • whpalmer4
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...
whpalmer4
  • whpalmer4
you lost a 3 in there somewhere...
anonymous
  • anonymous
t=3arc cos (h/7)/pi
whpalmer4
  • whpalmer4
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
anonymous
  • anonymous
So do I solve the problem three separate times but starting with 1cm first? Just sub it in for h?
anonymous
  • anonymous
So when I plugged in 1cm for h and solved I got t=0.4544
whpalmer4
  • whpalmer4
Yes, you just evaluate \[t = \frac{3}{\pi}\cos^{-1}(\frac{h}{7})\] for the 3 different values of \(h\)
whpalmer4
  • whpalmer4
hmm, that's not what I get, are you sure you are working in radians?
anonymous
  • anonymous
Hold on let me try again
whpalmer4
  • whpalmer4
If I plug that value of \(t\) into the formula, I get 6.22234
anonymous
  • anonymous
When I did it that way I got 12.3718
whpalmer4
  • whpalmer4
Okay,let's try this 1 step at a time. Punch in 1/7, what do you get?
anonymous
  • anonymous
8.1851?
whpalmer4
  • whpalmer4
Press the clear button — 1/7 = 0.142857142857142857...
anonymous
  • anonymous
Ohhh. Sorry haha ok i got that
whpalmer4
  • whpalmer4
now take the arc cosine of that...
anonymous
  • anonymous
Wait how would i set that up?
whpalmer4
  • whpalmer4
What kind of a calculator do you have?
anonymous
  • anonymous
Some online calculator my school provides. Dream calc?
whpalmer4
  • whpalmer4
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
anonymous
  • anonymous
0.9898
whpalmer4
  • whpalmer4
Oh, you didn't press the shift button - that's the result you would get for just cosine of 1/7
anonymous
  • anonymous
So for 2 its 0.9595
anonymous
  • anonymous
Sorry I dont do 2 i mean 3 3=0.9096
whpalmer4
  • whpalmer4
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?
whpalmer4
  • whpalmer4
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 \(h=1,3,5\) \[t=\frac{3}{\pi}\cos^{-1}(\frac{1}{7}) = \frac{3}{3.14159}\cos^{-1}{0.142857} \approx 1.363\] \[t=\frac{3}{\pi}\cos^{-1}(\frac{3}{7}) = \frac{3}{3.14159}\cos^{-1}{0.428571} \approx 1.077\] \[t=\frac{3}{\pi}\cos^{-1}(\frac{5}{7}) = \frac{3}{3.14159}\cos^{-1}{0.714285} \approx 0.74\]
whpalmer4
  • whpalmer4
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!

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