Find the work done by the force field F(x, y) = xi + (y + 6)j in moving an object along an arch of the cycloid r(t) = (t − sin(t))i + (1 − cos(t))j, 0 ≤ t ≤ 2π. Step 1 We know that the work done by the force field F in moving an object along the path C which is parameterized by the vector function r(t) is found by the following equation.

The work done by along is given by

where denotes the given path.

Since we already have the parameterization, all we need to do is compute the differential/length element:

Then the work is

i dont know sorry

step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is