A Ferris wheel 80 meters in diameter turns continuously, completing a single rotation once every 8 minutes. You must board the Ferris wheel at its lowest point from a platform located 5 meters above the ground. If you board the Ferris wheel at t=0, write and sketch a sinusoidal function to model your height above the ground after t minutes on the Ferris wheel. How high above the ground will you be after 5 minutes? How many minutes into the ride will it be when you first reach 35 meters above the ground?
Answers
Step-by-step explanation:
General form of a sine or cosine wave is:
y = ±A sin((2π/T) t) + B
y = ±A cos((2π/T) t) + B
where A is the amplitude, T is the period, and B is the vertical offset or midline.
The Ferris wheel is 80 meters in diameter or 40 meters in radius.
A = 40
The Ferris wheel turns once every 8 minutes.
T = 8
The lowest point is 5 meters above the ground, so the center of the Ferris wheel is 45 meters above the ground.
B = 45
At t=0, you're at the lowest point, so use -cos.
Therefore, the equation is:
y = -40 cos(2π/8 t) + 45
y = -40 cos(π/4 t) + 45
When t = 5:
y = -40 cos(5π/4) + 45
y = 20√2 + 45
y ≈ 73.3 meters
When y = 35:
35 = -40 cos(π/4 t) + 45
-10 = -40 cos(π/4 t)
1/4 = cos(π/4 t)
π/4 t ≈ 1.318
t ≈ 1.68 minutes
Related Questions
{−2x+7y=−7
−5x+14y=−7
Answers
Answer: x=7, y=2
Step-by-step explanation:
1. -2(-2x+7y=-7) -> 4x-14y=14
2. 4x-14y=14
-5x+14y=-7
3. -x = 7, x=7
4. -5(7)+14y=-7
5. -35+14y=-7
6. 14y=28, y=2
Answer: [tex]x=-7[/tex], [tex]y=-3[/tex]
Step-by-step explanation:
[tex]\left \{ {-2x+7y=-7} \atop {-5x+14y=-7} \right.[/tex]
multiply 2 at [tex]-2x+7y=-7[/tex]
[tex]-4x+14y=-14[/tex]
subtract [tex]-4x+14y=-14[/tex] and [tex]-5x+14y=-7[/tex]
[tex]x=-7[/tex]
put [tex]x=-7[/tex] at [tex]-2x+7y=-7[/tex]
[tex]7y=-21, y=-3[/tex]
Ella swims four times a week at her clubs pool. She swims the same number of labs on Monday, Wednesday, and Friday, and 15 laps on Saturday. She swims a total of 51 labs each week. How many laughs does she swim on Monday?
Answers
Given the function below, evaluate h(2) for x = -2
h(x) = -4x2 + x +1
Answers
2×2+31×1+1+1+1+1+11×4×4×4×4×4×4×4×4×4
Answers
Answer:
I think it is 13107200
Step-by-step explanation:
I think the answer might be 2,883,623. Hopefully, this helps you! :)
The area of a rectangular painting is 8613 cm?.
If the length of the painting is 99 cm, what is its width?
Answers
Answer:
The width is 87 cm
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
8613 = 99 * w
Divide each side by 99
8613 / 99 = 99 w /99
87 = w
The width is 87 cm
Answer:
Step-by-step explanation:
Given
The area of a rectangular painting=8613 cm^2
Length of painting=99cm
Solution
Area of the rectangular painting=8613
Length×width=8613
99×width=8613
Width=8613/99
Width =87cm
A tile factory earns money by charging a flat fee for delivery and a sales price of $0.25 per tile. One customer paid a total of $3,000 for 10,000 tiles. The equation y – 3,000 = 0.25(x – 10,000) models the revenue of the tile factory, where x is the number of tiles and y is the total cost to the customer.
Which function describes the revenue of the tile factory in terms of tiles sold?
Answers
The answer is 1.C 2.$500
How many proportional relationships are shown
Answers
Answer:
2 I think thats the answer
Step-by-step explanation:
Help!! Please thanks
Answers
Answer:
i think you have chosen the right answer i don't really know its tricky for me
Step-by-step explanation:
Find endpoints on a standard normal distribution with the given property. The area between is about 0.88 . Round your answers to three decimal places and place the endpoints in increasing order.
Answers
Answer:
-1.555 and 1.555
Step-by-step explanation:
For a standard normal distribution:
P(- Ƶ ≤ Z ≤ Ƶ) = 0.88
The normal distribution on the curve is symmetrical about Z = 0
Thus
P( -Ƶ ≤ Z ≤ 0) = P( 0 ≤ Z ≤ Ƶ)
However;
This implies that:
P( -Ƶ ≤ Z ≤ 0) + P( 0 ≤ Z ≤ Ƶ) = 0.88
2P ( 0 ≤ Z ≤ Ƶ) = 0.88
P( 0 ≤ Z ≤ Ƶ) = 0.44
P(Z ≤ Ƶ) - P( Z ≤ 0) = 0.44
Since P(Z ≤ 0) = 0.50
P(Z ≤ Ƶ) = 0.44 + 0.50
P(Z ≤ Ƶ) = 0.94
From the probability value table
z = 1.555
Thus the endpoints are:
-1.555 and 1.555
You move down 2 units and right 3 units. You end at (5,-5). Where did you start? On a coordinate plane plz need one more
Answers
Answer:
(2, -3)
Step-by-step explanation:
if move down 2 units, then y needs to move up 2 units
if move right 3 units, then x needs to move left 3 units
(5-3, -5+2)
(2, -3)
5z + 3n -z2 ; n = 4.5 , z = 6 PLZ answer this
Answers
Answer:
5(6)+3(4.5)- 6(2)= 31.5
Step-by-step explanation:
Answer:
hmmmmm
Step-by-step explanation:
Mr. Scruggs is going to donate $60 to the local animal shelter. If that $60 is 4/15
of the total amount of money he received for his birthday, how much money
did he receive in all?
Answers
5/25 in its simplest form
Answers
Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\frac{5}{25} =\frac{1}{5}[/tex]
Divide the numerator and denominator by their lowest common multiple which is 5 in this case
So 5 / 25 = 1 / 5
PLEASE HELP!!!! 50 POINTS!!!
Find the solution(s) of the following equation.
x^2 = 100/361
Choose all answers that apply:
a) x = -10/9
b) x = -1/6
c) x = 5/18
d) x = 5/9
e) none of the above
Answers
Answer:i think its b im not sure tho
Step-by-step explanation:
Answer: The answer is A) x= -10/19
Find the slope between the points. �. (5, −3) (7, 4)
Answers
Answer: slope is [tex]\frac{7}{2}[/tex] or 3.5
Step-by-step explanation:
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{4-(-3)}{7-5}[/tex] = [tex]\frac{7}{2}[/tex]
Answer:
[tex]\boxed {\boxed {\sf m= \frac{7}{2} \ or \ 3.5 }}[/tex]
Step-by-step explanation:
The slope formula is the change in y over the change in x.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this formula, (x₁, y₁) and (x₂, y₂) are the points given. We are given the points (5, -3) and (7,4). Therefore,
[tex]x_1=5 \\y_1= -3\\x_2=7 \\y_2=4[/tex]
Substitute the values into the formula.
[tex]m=\frac{4--3}{7-5}[/tex]
Solve the numerator.
4 - -3 = 4+3 = 7[tex]m=\frac{7}{7-5}[/tex]
Solve the denominator
7-5=2[tex]m=\frac{7}{2}[/tex]
[tex]m=3.5[/tex]
The slope between the points is 7/2 or 3.5
Convert 1AA from hexadecimal to decimal.
Answers
1AA = 426
What an odd class...
Answer:
426 in decimal.
Step-by-step explanation:
Step 1) Count the digits in 1AA, which in this case is 3 digits, and convert each digit to Hex.
Step 2) Starting from the last number in Step 1, multiply the first number with 1, the second number with 16, and the third number with 256.
Step 3) Add up all the numbers you got in Step 2 to get the answer.
Following the instructions above, your math should look like this:
10 x 1 = 10
10 x 16 = 160
1 x 256 = 256
10 + 160 + 256 = 426
Thus, we got the following answer:
1AA = 426
What is the solution set of \ x|x<-3\ cap\ x|x>5\ ?
Answers
Answer:
Let set A = {x|x<-3}
Let set B = {x|x>5}
The solution for set A could be graphically represented with a number line that contained an unshaded circle surrounding the integer -3 and all values to the left or less than -3 would be shaded.
The solution for set B could be graphically represented with a number line that contained an unshaded circle surrounding the integer 5 and all values to the right of 5 or greater than 5 would be shaded.
If you placed the two number lines close to each other, you would see that they do not intersect.
Thus there is no solution for the intersection of set A and set B as defined in the given problem.
Step-by-step explanation:
best estimate for 563 / 15
Answers
Answer: 37 8/15 or 37.53
Step-by-step explanation:
use math_way its amazing for math problems, if i could give a rating it would definitely get 5 stars.
its a website and a app i believe it can be used for ios and android
aka apple and everything else
btw i had to add that (_) <that in the name because it wont let me say it normally
45×(−10)×45 STEP explanation
Answers
Answer:
-20,250
Step-by-step explanation:
PEMDAS
Multiply left to right
45 * -10 * 45
45* -10
-450 * 45 =
-20,250
Suppose that the amount of snowfall per storm in Lincoln is normally distributed with µ = 4.2 inches and standard deviation µ = 2.3 inches (totally made up data). If the mayor decides that only the top 5% of storms should have school cancelled, what is the cutoff snowfall for school to be cancelled?
Answers
Answer:
7.9835
Step-by-step explanation:
Given that :
Mean snowfall per storm (µ) = 4.2 inches standard deviation (s) = 2.3 inches
Only the top 5% of storm should result in school being canceled :
Cut off snowfall for school to be canceled '
P(Z ≥ 5%) ; p(Z ≥ 0.05) = 1.645
Using the z relation :
Z = (x - m) / s
1.645 = (x - 4.2) /2.3
x - 4.2 = 2.3 * 1.645
x - 4.2 = 3.7835
x = 3.7835 + 4.2
x = 7.9835
Cut off snowfall for school to be canceled 7.9835
Answer:
hopes this photo helps
AC=39 Find the length of AB
Answers
Answer:
AB = 12
Step-by-step explanation:
tell whether the transformation appears to be a rigid motion. explain
Answers
Answer:
If you turn it or flip it over or move it it is essentially the same shape. If you try to stretch the paper or fold it you change what the shape is so it is not a rigid motion. Since the two circles are not the same size then it is not a rigid motion
What is the meaning of the base of the function y= log(x)?
A. As y increases by 1, x increases by 10.
B. As y increases by 1, x increases by a factor of 10.
C. As y decreases by 1, x increases by a factor of 10.
D. As y decreases by 1, x increases by 10.
Answers
If a function is defined by the formula y=1/2x + 3 and its domain is given by the set {-4,0,8}, then which of the following sets gives the function's range?
Answers
Answer:
y = {1, 3, 7}
Step-by-step explanation:
Given
y = ½x + 3
Domain: {-4, 0, 8}
Required
Determine the range of the function
To do this, we simply substitute each value of the domain in the given expression
We start with the first
Substitute -4 for x in y = ½x + 3
y = ½ * -4 + 3
y = -2 + 3
y = 1
Then 0
Substitute 0 for x in y = ½x + 3
y = ½ * 0 + 3
y = 0 + 3
y = 3
Lastly, 8
Substitute 8 for x in y = ½x + 3
y = ½ * 8 + 3
y = 4 + 3
y = 7
Hence, the range of the function is:
y = {1, 3, 7}
Answer:1,3,7
Step-by-step explanation:
Suppose that a company has fixed costs of $23 per unit and variable costs $10 per unit when 13,500 units are produced. What are the fixed costs per unit when 10,000 units are produced?
Answers
answer
32632 answer hai bro
Alexander spent a total of 12.5 hours on a science project for the Science Fair. His sister, Laura, spent 16.6 hours on a science project. How many more hours did Laura spend on her project than Alexander spent on his?
Answers
Answer:
4.1 I think
Step-by-step explanation:
I just subtracted in my head
Answer:
4.1 hours
Step-by-step explanation:
Laura spent 4.1 more hours on her project than Alexander spent on his. If we split each number into 2 parts (like this: 12.5 -> 12 and .5; 16.6 -> 16 and .6) then we can subtract 12 from 16 and .5 from .6 to get 4 and .1. we add those together to get 4.1
Simplify the expression:
8(x - 5) + 7(3x + 4)
Answers
Answer:
29x-12
Step-by-step explanation:
29x-12
Step-by-step explanation:
8•x=8×
8•-5=-40
7•3x=21x
7•4=28
-40+28=-12
21x+8x=29x
Explanation for solving the following equation
1/2(f+4)=8
Answers
Divide the whole thing by 1/2 to get rid of it.
f + 4 = 16
Subtract 4 on both sides
f = 12
Which coordinates represent the plotted point? Check all that apply.
Answers
Answer:Its A,C,E or 1,3,5
Step-by-step explanation:
Got it right in Ed
Answer:
A C E
Step-by-step explanation:
Y=2× Y=×+1
A: (2/3, 1/3)
B: (1,2)
C: (2,1)
D: (1/3, 2/3)
Answers
Answer:
The answer is B: (1,2)
Step-by-step explanation:
(solved using elimination method)
-2x+y=0
y=x+1
-x+y=1
-2x+y=0
x+y=-1
-x=-1
x=1
-1+y=1
y=2
(x,y)=(1,2)