Rachel is bowling with her friends. her bowling ball has a radius of 4 inches. as she bowls she tracks the location of the finger hole above the ground. she starts tracking the location when the finger hole is at the 12 o'clock position and she notices that she got some backspin on the ball and it rotates counter-clockwise.

Question Continuation

The finger hole changes by 45 degrees.

Define a function, f, that gives the height of the finger hole above the ground (in inches) in terms of the angle of rotation (measured in radians) it has swept out from the 12 o'clock position.

f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

Step-by-step explanation:

Given

Let represent radius

r = 4 inches

Considering that she starts tracking the location when the finger hole is at the 12 o'clock; this means that the angle measurement at this point is 0°.

Let θ represent the angle

At 12 o'clock mark

θ = 0

When the finger hole changes by 45 degrees

θ = 45°

Convert 45° to radians

θ = 45° * π/180

θ = π/4

So, angle θ is such that θ∈[0, π/4]

This can be represented as

0 ≤ θ ≤ π/4

Calculating the measure of f(θ) in polar coordinates

When θ = 0, f(θ) = r (i.e. the current position of the bowl)

When θ = π/2, f(θ) = rcosθ

This is so because f(θ), being the function of the height is a measure of the radius* cos(θ)

Taking measurement of f(θ) from 0 to π/2

f(θ) = r + rcosθ

f(θ) = r(1 + cos(θ))

So, f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

its a straight line parallel to the time axis