A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
The force F (in newtons) of a hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters) that the cylinder is extended in its cycle. The domain of F is [0, π/3], and F(0) = 900
Find the average force exerted by the press over the interval [0, π/3]. (Round your answer to one decimal place.)
anonymous
 one year ago
The force F (in newtons) of a hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters) that the cylinder is extended in its cycle. The domain of F is [0, π/3], and F(0) = 900 Find the average force exerted by the press over the interval [0, π/3]. (Round your answer to one decimal place.)

This Question is Closed

marco26
 one year ago
Best ResponseYou've already chosen the best response.0Perhaps you can use: \[F _{ave}=\frac{ f(x _{final})f(x _{initial}){} }{ x _{final}x _{initial} }\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0we have \(F(x) = k \sec^2 x\) and \(F(0) = 900 \implies k = 900\) so you want the average value of \(F(x) = 900 \sec^2 x\) over the interval \(0 \le x \le \frac{\pi}{3}\) dw:1443517655585:dw for the average, geometrically you want to find the area under the \(F=900\sec^2(x)\) curve in the interval and then find the rectangle with equivalent area. the height of that rectangle is the average value of F through the cycle in physical terms, the work done by the piston is the area under the \(F=900\sec^2(x)\) curve, ie \(W=\int F dx\). the average value of F is the constant force F that would do the same amount of work: \(W=\int F dx = \bar F\times x\). in either case you can say average force \(\bar F \) is \[\large \bar F = \dfrac{\int\limits\limits_{0}^{\frac{\pi}{3}} F(x) \; dx}{\frac{\pi}{3}} = \dfrac{900\int\limits_{0}^{\frac{\pi}{3}} \sec^2x \; dx}{\frac{\pi}{3}} \] [NB typo in drawing, it's \(sec^\color{red}2 x\)]
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.