Annabelle’s bicycle has a wheel radius of 13 inches. She places a sticker on the wheel so that its minimum height above the ground is 0.5 inches. When she rides her bicycle, the wheel completes 90 revolutions every minute. The sticker begins at its minimum height above the ground. Which equation models the height in inches of the sticker after x minutes? y = 0.5 sine (180 pi x) + 13 y = 12.5 sine (180 pi x) + 13 y = 0.5 sine (180 pi x minus StartFraction pi Over 2 EndFraction) + 13 y = 12.5 sine (180 pi x minus StartFraction pi over 2 EndFraction) + 13

Step-by-step explanation:

In order to solve this we can start by drawing a sketch of the problem (see attached picture)

So fist, let's take the general form of a sinusoidal movement:

where:

A= amplitude

= angular frequency

x= time

= horizontal shift

b= vertical shift.

In this case, the amplitude will be the maximum distance between the center of the wheel and the highest or lowest point of the trajectory, in this case:

A= 13in - 0.5in =12.5 in

The angular frequency is how many radians the wheel will turn in a minute, so we get:

Generally, the sin function will start at the center of the circular movement. In this case, since it starts on the lowest point, we can say that the graph moves right by , so in this case:

and finally, the vertical shift is the distance between the center of the circular movement and the ground so in this case:

b=13in

so when putting it all together we get our equation to be:

518,400

step-by-step explanation:

the area is multiplying all the given measurements together.

40 * 18 * 30 * 24 = 518,400

answer: since the question is talking about growth you have to use the growth formula which is inital amount (1 + growth)^time

step-by-step explanation:

the intial amount is 1200, the growth is 4.8, and the time is 7. plug those numbers into the equation, also i think you have to change 4.8 into a percent. but, i have forgotton how to do that. if this is a online class go on to the lesson.