Question

A spring has a natural length of 1 meter and force of 10 N is required to hold a spring stretched from 1 meter to 1.5 meters. (a) Find the spring constant k, in N/m. (b) Find the work done, in Joules, in stretching the spring 2 meters beyond its natural length. F = kx 10N = k(0.5) k = 20 ??² kx dx = kx²/2 |?² = 20x²/2 |?² = 40 J Consider the function f(x) = 1/?x on the interval [1, 4]. (a) Find the average value f_ave of f on the given interval. (b) Find c such that f_ave = f(c). f_ave = 1/(4-1) ??? 1/?x dx = 1/3 ??? 1/x^(1/2) dx = 1/3 [2 ? x^(1/2)] |?? = [2/3(4)^(1/2) - 2/3(1)^(1/2)] 1/?c = 1/6 c = 36

          A spring has a natural length of 1 meter and force of 10 N is required to hold a spring stretched from 1 meter to 1.5 meters.
(a) Find the spring constant k, in N/m.
(b) Find the work done, in Joules, in stretching the spring 2 meters beyond its natural length.
F = kx
10N = k(0.5)
k = 20
??² kx dx
= kx²/2 |?²
= 20x²/2 |?²
= 40 J
Consider the function f(x) = 1/?x on the interval [1, 4].
(a) Find the average value f_ave of f on the given interval.
(b) Find c such that f_ave = f(c).
f_ave = 1/(4-1) ??? 1/?x dx
= 1/3 ??? 1/x^(1/2) dx
= 1/3 [2 ? x^(1/2)] |??
= [2/3(4)^(1/2) - 2/3(1)^(1/2)]
1/?c = 1/6
c = 36

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A spring has a natural length of 1 meter and force of 10 N is required to hold a spring stretched from 1 meter to 1.5 meters.
(a) Find the spring constant k, in N/m.
(b) Find the work done, in Joules, in stretching the spring 2 meters beyond its natural length.
F = kx
10N = k(0.5)
k = 20
??² kx dx
= kx²/2 |?²
= 20x²/2 |?²
= 40 J
Consider the function f(x) = 1/?x on the interval [1, 4].
(a) Find the average value fave of f on the given interval.
(b) Find c such that fave = f(c).
fave = 1/(4-1) ??? 1/?x dx
= 1/3 ??? 1/x^(1/2) dx
= 1/3 [2 ? x^(1/2)] |??
= [2/3(4)^(1/2) - 2/3(1)^(1/2)]
1/?c = 1/6
c = 36

Added by Carolina J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/30/2023

Step 1

We are given that the spring has a natural length of 1 meter and a force of 10 N is required to stretch it to 1.55 meters. We can use Hooke's Law to find the spring constant k: F = kx where F is the force applied, k is the spring constant, and x is the Show more…

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