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

Answer:

[tex]y=12.5 sin(180\pi x-\frac{\pi}{2})+13[/tex]

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:

[tex]y=Asin(\omega x+\phi)+b[/tex]

where:

A= amplitude

[tex]\omega[/tex]= angular frequency

x= time

[tex]\phi[/tex] = 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:

[tex]\omega=\frac{90 rev}{min}*\frac{2\pi rad}{1 rev}[/tex]

[tex]\omega=180\pi rad/min[/tex]

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 [tex]\frac{\pi}{2} rad[/tex], so in this case:

[tex]\phi=-\frac{\pi}{2}[/tex]

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:

 [tex]y=12.5 sin(180\pi x-\frac{\pi}{2})+13[/tex]

You toss a coin in the air and it lands on the table. What is the probability that it lands on heads? *​

A farmer is trying to decide how many acres of land he has planted by
finding the area, A, of his plot. x represents a measuring chain he is
using. If the plot has length (5x – 3) and width (2x + 7), which of the
following is the area in terms of x?
F 10x2 + 41x-21
H 10x2 + 29x - 21
G. 7X2 + 7x + 4
J. x2 - 6x +4

find x

help please, asap.

Need help ASAP!!!!!!!

madyson has 2 vases of flowers. Each vase has 6 flowers. Madyson must divide the flowers equally into three vases. how many flowers will be in each vase?

A 6-foot ladder is placed against a wall with its base 2
feet from the wall. How high up the wall is the top of the
ladder? (HINT: Draw a diagram to help you visualize
the problem.)

Emily ha 6 pounds of grapes. She splits the grapes into smaller 1/3 pound bunches. How many bunches of grapes can she make ?

Find the surface area of the prism.
Please help

If a car's cost, when new, is
$15,000, the rate of
depreciation is 30%, how
much will the car be worth in
6 years?

Find the area of this triangle.
Round to the nearest tenth.
12 cm
33°
5.5 cm
[?] cm2

−2(5d−9f)+7f−10(−9f−7d)

A 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. How many containers of sugar will the 9 pound bag create? (sorry i forgot the 2/3 last time!)

A circular patio has a radius of 4 yards. The patio is expanded so that the
radius increases by 2 yards. By how many square yards does the area of the
patio increase?

send answer really need it

PLEASE HELP ME THANKS!

Which of the following choices shows the proper use of the distributive property?
оооо
-2(6x - y) = -12x + 2y
-2(6x - y) = 12x + 2y
-2(6x - y) = 12x - 2y
-2(6x - y) = -12x - 2y
What’s the answer

38% of what number is 171?

Elizabeth planted a garden in a 16 foot by 8 foot area. To calculate the square foot area of the garden, she multiplied 16 by 8 and got a product of 128 square feet Which equation could Elizabeth use to check her answer? A) 16 x 8 = 128 B) 128 - 8 = 16 © 128 + 8 = 136 D. 128 - 8 = 120 please help​

QUESTION 5 of 10: Throughput is the number of units a machine or process can produce in a given time. Cycle time is the time to produce
one unit. If the cycle time of your machine is 35 seconds and it runs 24/7, what is the throughput for a year period?
O a) 901,029
Ob) 969,623
c) 1,180,336
d) 1,173,322

Hay 12 canicas en una bolsa y 6
de ellas son verdes. Si se elige
una canica, ¿cuál es la
probabilidad de que sea verde?

What is the volume of the cylinder shown? (Use 3.14 for it.)


6.838.92 in.^3

1.413.56 in^3

1.243.44 in^3

11.190.8 in.^3

How to find surface area of a composite figure

How much is 2/9th of 234.900?

What is the answer please

Susannah is buying lunch for her friends at a restaurant. The bill is $50, and she wants to
leave an 18% tip.

help me and I’ll give you brainliest

14
23
22.7
Find the perimeter

What is the volume of the square pyramid, in cubic inches?

Rotate rectangle CDEF with C{-4.0). D1-1,-1), E(-3,-7), and F(-6,-6) 90° counterclockwise about the origin. What are the coordinates of ΕΡ JU​

3rd 9-Week Exam
Question: 1-1
Monica is using a coordinate plane to make a design in art class. She wants to reflect a line segment across the x-
axis as part of the design. The line segment has an endpoint at (-7,5) and is 5 units long. Which two ordered pairs
could be the coordinates of the endpoints of the reflection of the line segment?