Ethan is observing an amusement park ride where the riders go around in a counterclockwise circular motion. The
carts take 2 seconds to complete a full rotation. The center of the ride is 24 feet above the ground as shown in the
diagram, and the cart Ethan is observing is labeled X
Answers
A sinusoidal equation can be used to describe the height because the height depends on a periodic motion, and the equation can be written as:
h(t) = 13ft*sin(pi*t) + 24ft
Why a sinusoidal equation can be used?Remember that the sine function has a periodicity, such that:
sin(x + 2pi) = sin(x).
So, for a circle where if you do a complete rotation you end in the initial place, so there can be a relation between the height and a sinusoidal equation.
Notice that the initial position is 24ft above the ground, so we can write this, at the moment, as:
h(x) = Asin(n*t) + 24ft
A is the amplitude, it defines the maximum height and minimum height, both depend on the radius (the maximum height is 24ft plus the radius, the minimum height is 24ft minus the radius) then we write:
h(t) = 13ft*sin(kt) + 24ft
k depends on how much time takes to do a full rotation. We know that the sine function does a "complete cycle" in 2pi, while the wheel does a full rotation in 2 seconds, then we have that:
k*2 = 2pi
k = (2pi)/2s = pi
Then the sinusoidal equation that represents the height is:
h(t) = 13ft*sin(pi*t) + 24ft
If you want to learn more about sinusoidal equations, you can read:
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Related Questions
Can you help please I really need it
Answers
Answer:
65cm
Step-by-step explanation:
100cm= 1 metre
?=2.5m
=2.5*100=250cm
250-(60+35+90)=65cm
remaining length=65cm
What is 1 3/8 equals to
Answers
Answer:
1.375 in decimal form
Step-by-step explanation:
Points J and K are midpoints of the sides of triangle FGH.
Triangle F G H is cut by lines segment J K. Point J is the midpoint of side G H. Point K is the midpoint of side H F. Line segments G J and J H are congruent. Line segments H K and K F are congruent. The Length of J K is 2 y + 5 and the length of G F is 5 y + 3.
What is the value of y?
2
5
7
8
Answers
Answer:
C. 7
Step-by-step explanation:
Points J and K are midpoints of the sides of triangle FGH.
=> JK = 1/2FG
2y + 5 = 1/2(5y + 3)
4y + 10 = 5y + 3
5y - 4y = 10 - 3
y = 7
The value of y is 7 for the given triangle.
What are the properties of Triangle?The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
We know that GJ = JH, and HK = KF.
Also, J and K are midpoints of GH and HF, respectively.
Therefore, we can say that:
GJ + JH + HK + KF = GF
2(GJ + HK) = GF
2(2y + 5) = 5y + 3
4y + 10 = 5y + 3
y = 7
Therefore, the value of y is 7.
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A triangle is equilateral if
sides are the same length.
Answers
What is the ratio of the Patio?
Answers
Answer:
B
Step-by-step explanation:
the are of the square would be: 4*6=24
the are of one triangle would be: (6*2)/2=6 (12 in total because there are two triangles
to find the whole area, you add 24 and 12 which is B) 36 meters squared
Find the area of a triangle
Answers
Answer:
½*b*h
Step-by-step explanation:
½*base*height
you can use the above formula to answer the following questions.(9w^2+7w-2)+(8w^2-8w-7)-(-5w^2+5w+4)
Answers
Step-by-step explanation:
Our expression;
[tex](9w^2+7w-2)+(8w^2-8w-7)-(-5w^2+5w+4)[/tex]
Also represented as after using the distributive property;
[tex]9w^2+7w-2+8w^2-8w-7+5w^2-5w-4[/tex]
Simplify;
[tex]9w^2+7w-2+8w^2-8w-7+5w^2-5w-4[/tex]
[tex]22w^2+7w-2-8w-7-5w-4[/tex]
[tex]22w^2-6w-2-7-4[/tex]
[tex]22w^2-6w-13[/tex]
Answer:
22w² - 6w - 13
Step-by-step explanation:
Given expression: (9w² + 7w - 2) + (8w² - 8w - 7) - (-5w² + 5w + 4)
Step-1: Open the parenthesis
⇒ (9w² + 7w - 2) + (8w² - 8w - 7) - (-5w² + 5w + 4)⇒ 9w² + 7w - 2 + 8w² - 8w - 7 + 5w² - 5w - 4Step-2: Combine like terms
⇒ 9w² + 7w - 2 + 8w² - 8w - 7 + 5w² - 5w - 4⇒ w²(9 + 8 + 5) + w(7 - 8 - 5) + (-2 - 7 - 4)Step-3: Simplify the expression
⇒ w²(9 + 8 + 5) + w(7 - 8 - 5) + (-2 - 7 - 4)⇒ w²(22) + w(-6) + (-13)⇒ 22w² - 6w - 13Therefore, the simplified expression is 22w² - 6w - 13.
Really Easy, Help pleaseee
Answers
1 minute = 0.25km
Step-by-step explanation:
divide both numbers that were given by 8. 8÷8 is 1 and 2÷8 is 0.25.
A server makes $200 a week working at a local restaurant. The server saves 35% of the $200 weekly earnings each week for 4 weeks.
If the server saves 78 of the 5th week’s $200 earnings, how much money will the server have saved in total after the 5 weeks?
please i need help and i taking a test
Answers
Answer:
He would of saved 455$
Step-by-step explanation:
Because for 4 weeks he saved 35% of 200$ which would be 70 and 70+70+70+70 is 280$ and then he saved 175 dollars on the 5th week because 7/8 of 200 is 175 so 280+175= 455
I hope this helps!
Write this in an equation: 5 less than a number is twice the sum of that number and 9
Answers
Answer:
n-5=2n+9
Step-by-step explanation:
the squar of any rational number is non negative
Answers
Yes that is true.
The square of 2 is 4.
The square of -3 is 9.
[tex]\mathbb{FINAL\:ANSWER:}[/tex]
[tex]\huge\boxed{\sf{True}}[/tex]
[tex]\mathbb{SOLUTION\:WITH\:STEPS:}[/tex]
Hi! Hope you are having a nice day!
Yes, the square of a rational number is always positive.
We know that a negative times a negative equals a positive only.
Well, a negative squared also equals a positive.
For example, (-4)² is equal to 16.
Because
(-4)×(-4)=16
A negative times a negative is a positiveHope you could understand everything.
#CarryOnLearning
What is the y-intercept in y= -2x + 5
Answers
Answer: 5
Step-by-step explanation:
the y intercept is the "b" value in the form y = mx + b
A convex pentagon has interior angles that measure 60, 80, 120, and 140. What is the measure of the fifth interior angle?
Answers
A convex pentagon has interior angles that measure 60, 80, 120, and 140. What is the measure of the fifth interior angle?
Explanation -:Given -
First interior angle = 60°Second interior angle = 80°Third interior angle = 120°Fourth interior angle = 140°To Find -
Fifth interior angleSolution -
Let us assume fifth interior angle as x
We know,
Sum of interior angles of a pentagon is 540°
60° + 80° + 120° + 140° + x° = 540°
→ 400° + x° = 540°
→ x° = 540° - 400°
→ x = 140°
Fifth interior angle of a pentagon = 140°
[tex] \rule{185pt}{7pt}[/tex]
The ratio of the number of pears to the number of oranges in a basket
is 5:3. The rest of the fruits are apples. There are 54 more pears than
oranges and 3 more apples than oranges.
(a) How many pears are there in the basket?
(b) What percentage of the fruits are apples?
Answers
Answer:
(a) 135
(b) 28%
Step-by-step explanation:
We can write equations relating pears to oranges, solve them, and then find the number of apples. Let p, o, and 'a' represent the numbers of pears, apples, and oranges.
p/o = 5/3 . . . . . the ratio of pears to oranges is 5:3
p -o = 54 . . . . . there are 54 more pears than oranges
a -o = 3 . . . . . . there are 3 more apples than oranges
__
a)Multiply the first equation by 3/5o to get ...
3/5p = o
Substitute that into the second equation:
p -(3/5)p = 54
2/5p = 54 . . . . . . simplify
p = 54(5/2) = 135 . . . . multiply by 5/2 to get the number of pears
There are 135 pears in the basket.
__
b)a = 3 +o = 3 +3/5p = 3 +3/5(135) = 3 +81 . . . . solve for the number of apples
a = 84
The percentage of fruits that are apples is ...
apples/total = 84/(135 +81 +84) = 84/300 = 28/100 = 28%
28% of the fruits are apples
When I see an equation with parentheses, I need to use the Distributive Property.
O True
O False
Answers
Janelle plans to paint her bedroom, which is the shape of a
rectangular prism. Its length is 10 feet, its width is 12 feet, and the
ceilings are 9 feet tall. She does not need to paint the floor or ceiling. How many square feet of wall space will she be covering?
Answers
Answer:
19 feet tall
Step-by-step explanation:
The table shows the approximate height of an object x seconds after the object was dropped. the function h(x) = –16x2 100 models the data in the table. a 2-column table with 5 rows. the first column is labeled time (seconds) with entries 0, 0.5, 1, 1.5, 2. the second column is labeled height (feet) with entries 100, 96, 84, 65, 37. for which value of x would this model make the least sense to use? –2.75 0.25 1.75 2.25
Answers
The value of x for which this model will make the least sense to use is at x=-2.75 seconds.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function that is given to us is h(x) = –16x²+100 where x is the time in seconds.
Now, use the function to know the height of the object, therefore, the height of the object can be written as,
Time, t₁=0
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(0)=0+100\\\\h_1=100[/tex]
Thus, the height of the object when the time is 0 seconds is 100.
Time, t₂=0.5
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(0.5)=-4+100\\\\h_2=96[/tex]
Thus, the height of the object when the time is 0.5 seconds is 96.
Time, t₃=1
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(1)=-16+100\\\\h_1=84[/tex]
Thus, the height of the object when the time is 1 second is 84.
Time, t₄=1.5
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(1.5)=-36+100\\\\h_4=64[/tex]
Thus, the height of the object when the time is 1.5 seconds is 64.
Time, t₅=2
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(2)=0+100\\\\h_5=36[/tex]
Thus, the height of the object when the time is 2 seconds is 36.
Now as we can see that the error in the height of the object can be a maximum of 1, therefore, for different values of x, the change in height will be,
Time, t₆= -2.75
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(-2.75)=-121+100\\\\h_6= -21[/tex]
Thus, the height of the object when the time is -2.75 seconds is -21.
Hence, the value of x for which this model will make the least sense to use is at x=-2.75 seconds.
Learn more about Function:
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Answer:
-2.75
Step-by-step explanation:
A
Consider a game board that has 49 squares. You place 1 grain of wheat on the first square, 2 on the next, 4 on the next, 8 on the next, and so on to the 49th square. How many total grains of wheat will there be? Write your answer using scientific notation.
Answers
Approximately 5.6 x 10¹⁴ grains of wheat in scientific notation.
Describe Geometric Series?A geometric series is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed constant. This constant is called the common ratio, and it is denoted by the letter "r".
The formula for the sum of the first n terms of a geometric series is:
S_n = a(1 - rⁿ)/(1 - r)
where S_n is the sum of the first n terms, a is the first term of the sequence, r is the common ratio, and n is the number of terms in the series.
The number of grains of wheat on each square of the board can be found by raising 2 to the power of the square number minus 1. For example, the number of grains of wheat on the first square is 2⁰ = 1, the number on the second square is 2¹ = 2, the number on the third square is 2² = 4, and so on.
So, the total number of grains of wheat on the board is the sum of 2⁰ + 2¹ + 2² + ... + 2⁴⁸. This is a geometric series with first term 1 and common ratio 2. Using the formula for the sum of a geometric series, the total number of grains of wheat is:
2⁰ + 2¹ + 2² + ... + 2⁴⁸ = (2⁴⁹ - 1)/(2 - 1) = 2⁴⁹ - 1
This is approximately 5.6 x 10¹⁴ grains of wheat in scientific notation.
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help please i beg you!!
Answers
Answer:
Step-by-step explanation:
-x + 3y =9
substitute y with 2/3x as mentioned in the question
so,
-x+3 (2/3x) = 9
cancelling 3 we get..
-x+2x=9
x=9
hope it helps
thanks
Answer:
y = 6
Step-by-step explanation:
- x + 3y = 9 ( add x to both sides )
3y = 9 + x → (1)
y = [tex]\frac{2}{3}[/tex] x ( multiply both sides by 3 to clear the fraction )
3y = 2x → (2)
substitute 3y = 2x into (1)
2x = 9 + x ( subtract x from both sides )
x = 9
substitute x = 9 into (1)
3y = 9 + 9 = 18 ( divide both sides by 3 )
y = 6
Solve for x and y.
y
6
X
2
X=
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answers
Answer:
How to solve your problem
Step-by-step explanation:
1.1 x2 multiplied by x1 = x(2 + 1) = x3
Final result
y6x3
Why is math literacy important?
Answers
Answer:
Math literacy (also known as numeracy) means having the ability to problem-solve, reason, and analyze information.
Step-by-step explanation:
Each problem below gives the endpoints of a segment. Find the coordinates of the midpoint of the segment.
a. (-3,11) and (5,6)
b. (-4,-1) and (8,9)
Answers
Answer: A
Step-by-step explanation:
The Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour. City Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal. The family made a graph of the two offers. When would City Movers be the better deal?
Answers
If the Thompsons need the movers for more than 6 hours, City movers would be the better deal. Therefore, option D is the correct answer.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Given that, the Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour.
Let the number of hours be x.
Now, 30+15x
Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal
72+8x
From the graph, both the movers have same charge at 6th hour and City movers charge is decreasing then compare to Town Movers.
Therefore, option D is the correct answer.
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A shark can swim at a speed of 172 miles per hour. At this speed, how far does it travel in 5 hours? 2
Answers
Answer:
860 miles
Step-by-step explanation:
172 miles per hour x 5 hours = 860 miles
Answer:
860 miles
Step-by-step explanation:
172 x 5 = 860
the shark has moved 172 miles in one hour, so to figure out how far it has traveled in 5 you can multiply the speed by the time.
find the centrroid of the triangle with the given vertices F(1, 5), G(-2, 7) and H(-6, 3)
Answers
[tex]\qquad \textit{Centroid of a Triangle} \\\\ \left(\cfrac{x_1+x_2+x_3}{3}~~,\cfrac{y_1+y_2+y_3}{3}~~ \right)\quad \begin{cases} F(\stackrel{x_1}{1},\stackrel{y_1}{5})\\\\ G(\stackrel{x_2}{-2},\stackrel{y_2}{7})\\\\ H(\stackrel{x_3}{-6},\stackrel{y_3}{3}) \end{cases} \\\\\\ \left( \cfrac{1-2-6}{3}~~,~~\cfrac{5+7+3}{3} \right)\implies \left( \cfrac{-7}{3}~~,~~\cfrac{15}{3} \right)\implies \left( -2\frac{1}{3}~~,~~5 \right)[/tex]
what is the volume of 5cm 2cm 8cm.
Answers
Answer:
80 cm
Step-by-step explanation:
(5 x 8) x 2
40 x 2
80 cm
Answer:
80cm
Step-by-step explanation:
5x8=40x2=80cm
Help help help help help help help help
Answers
Answer:
Roughly 10%
Step-by-step explanation:
We just need to reduce this fraction: 13/119
It is in the lowest terms already, so now we need to make this fraction a percent.
13/119 = 10.12
10.12 ≈ 10%
Kaitlyn solved the equation for x using the following calculations. Negative 5. 4 x = 12. 2. Minus 5. 4. X = 6. 8. What error, if any, did she make? She should have added 5. 4 to each side. She should have added the inverse of 5. 4 to each side. She made a computational error when she subtracted 5. 4 from 12. 2. She should have added 12. 2 to each side.
Answers
The value of x is 17.6. She should have added 5.4 on both sides to get the correct value of x. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Kaitlyn solved the equation for x using the following calculations.
[tex]\rm -5.4 + x =12.2[/tex]
and she did the calculation will be
[tex]\rm -5.4x = 6.8[/tex]
The mistake she did in this equation is the plus sign is removed between the -5.4 and x. And she subtracted 5.4 from 12.2.
The correct solution of the equation is to add both sides 5.4. Then we have
[tex]\begin{aligned} \rm -5.4 + x+5.4 &=12.2+5.4\\\\\rm x &= 17.6\end{aligned}[/tex]
More about the linear system link is given below.
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Factor x^2 + 9 in the complex numbers.
Answers
Answer:
Multiply
3
by
−
1
.
(
x
+
3
i
)
(
x
−
3
i
)
What is the area of the shaded region of the figure pictured? Round your answer to the nearest tenth.
Answers
Answer:
use Pythagoras to find diameter of circle.
use half of diameter as radius to find area of circle.
subtract area of square from area of circle.
the steps are very simple so I didn't want to waste time drawing it out. added a photo outlining each step for you. feel free to ask if you need a step explained