Casey boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 5.6 radians per minute and has a radius of 50 feet. The center of the Ferris wheel is 55 feet above the ground. Let t represent the number of minutes since the Ferris wheel started rotating. a. Write an expression (in terms of t) to represent the varying number of radians θ Ryan has swept out since the ride started.
b. Write an expression (in terms of t) to represent Ryan's height (in feet) above the ground.

Solution :

It is given that :

Casey boarded a Ferry wheel at position of 3 'o' clock.

The angular speed of the Ferry wheel = 5.6 radians per minute

The radius of the Ferry wheel = 50 feet

The height of the center wheel of the Ferry from the ground = 55 feet

Let the number of minutes be = t

a). The expression of the varying number of radians θ is given by :

After t minutes,  θ = angle swept

                           θ = 5.6 t radians

b). Finding the height from the center of the wheel.

We know that : y = r sin θ

Given r = 50 feet

So, y = 50 sin (5.6 t) feet

Therefore, the height above the ground can be found by :

h = y + 55 (from ground)

h = 50 sin (5.6 t) + 55   feet

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing

step-by-step explanation:

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.