A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
P(t)= 100 sin((pi t)/2)+500
Calculate the maximum value for t.
I have derived the function to
P'= 50pi cos((pi t)/2)
anonymous
 5 years ago
P(t)= 100 sin((pi t)/2)+500 Calculate the maximum value for t. I have derived the function to P'= 50pi cos((pi t)/2)

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let P' equal 0 and solve for t. 0 = 50pi cos(pi t / 2) cos(pi t / 2) = 0 pi t / 2 = arccos 0 = pi / 2 + 2kpi t = 1 + 4k; where k is any integer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, i havnt learnt arccos but the textbook says "Take the first two values to see which is minimum" pi t/2 = pi/2 or 3pi/2 t= 1,3 I dont understand this part.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, the text is telling you to see which one produces a maximum value. Either t = 1 or t = 3 produces a maximum value. If you put t = 1 into the original equation P(1) = 100sin(pi (1)/2) + 500, you will get a maximum P = 600. If you put t = 3 into the original equation P(3) = 100sin(pi (3)/2) + 500, you will get a minimum P = 400. The t = 1 is clearly the maximum value. Is this Calc 1 / AB? I'd imagine you would have learned how to calculate arc cosines in trigonometry/precalculus.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Uh, i live in Australia so i would imagine that the subjects would be different. But yeah, i want to know how the textbook got t=1,3?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, I'm sorry. Anyway, I guess the values t = 1 and t = 3 are the first values that would come to mind that would produce a maximum/minimum. There's nothing really special about them though. If you plug any integer k into t = 1 + 4k to get a number t. That number t will produce a maximum value. Likewise, if you plug any integer k into t = 3 + 4k to get a number t, that number t will produce a minimum value.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh so, for any trig max/min problems the t= 1,3 would most likely be max/ win?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It depends on what is inside the sine. For example, if P = 100sin(t) + 500, then, the maxima would occur at t = pi / 2 + 2pi; the minima would occur at t = 3pi / 2 + 2pi. It could also change if the sine was a cosine instead. It takes a fundamental understanding of trigonometry to see the relationship. But no, t = 1, 3 are not always the max and min t values...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh right, guess i need to brush up on trig!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we cant find the max value of t . it will infinite as domain of this function is (infinite, infinite) . we need not to find out maxima or minima of p(t)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Of course we can't find the max value of t. I assumed we were talking about relative extrema.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.