Find a parametric representation for the part of the cylinder y2 + z2 = 49 that lies between the planes x = 0 and x = 1. x = u y = 7cos(v) z = 0 ≤ v ≤ 2π ≤ u ≤

The equation for z for the parametric representation is   and the interval for u is .

Step-by-step explanation:

You have the full question but due lack of spacing it looks incomplete, thus the full question with spacing is:

Find a parametric representation for the part of the cylinder , that lies between the places x = 0 and x = 1.

Thus the goal of the exercise is to complete the parameterization and find the equation for z and complete the interval for u

Interval for u

Since x goes from 0 to 1, and if x = u, we can write the interval as

Equation for z.

Replacing the given equation for the parameterization on the given equation for the cylinder give us

Solving for z, by moving to the other side

Factoring

So then we can apply Pythagorean Theorem:

And solving for sine from the theorem.

Thus replacing on the exercise we get

So we can take the square root of both sides and we get

answer: the correct answer is -32

step-by-step explanation: