where h is the height of the car in metres, t is the time that has elapsed in minutes and a, b and c are constants.
Find values for a, b and c that will effectively model your motion on the big wheel.
Answers
The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached
The values of the constants in the sinusoidal function, h = a + b·(c·t) are;
a = 30
b = -20
c = π/1.5
What is a sinusoidal function?A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.
The diameter of the Ferris wheel = 40 m
The location of the axle above the ground = 30 m
The time it takes to make a complete a rotation = 3 minutes
The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;
h = a + b·cos(c·t)
The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.
Therefore;
At t = 0, h = 30 - 40/2 = 10
h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b
a + b = 10
Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;
a = 30
a + b = 10, therefore;
b = 10 - a
b = 10 - 30 = -20
b = -20
At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50
50 = a + b·cos(1.5·c)
50 = 30 - 20 × cos(1.5·c)
20 × cos(1.5·c) = 30 - 50 = -20
cos(1.5·c) = -1
cos(π) = -1
Therefore; 1.5·c = π
c = π/1.5
The equation is therefore;
h = 30 - 20·cos((π/1.5)·t)
a = 30, b = -20, c = π/1.5
Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel
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Related Questions
Which functions have an axis of symmetry of x = –2? Check all that apply.
f(x) = x2 + 4x + 3
f(x) = x2 – 4x – 5
f(x) = x2 + 6x + 2
f(x) = –2x2 – 8x + 1
f(x) = –2x2 + 8x – 2
Answers
The quadratic functions that have an axis of symmetry at x = -2 are given as follows:
f(x) = x² + 4x + 3.f(x) = -2x² - 8x + 1.How to obtain the axis of symmetry of a quadratic function?The standard definition of a quadratic function is given by the rule presented as follows:
y = ax² + bx + c, in which a is different of zero.
The axis of symmetry is given by the x-coordinate of the vertex, hence it's equation is defined as follows:
x = -b/2a.
Meaning that the correct options are given by the first and by the fourth options in this problem.
For the first function, we have that:
a = 1, b = 4.
Hence the axis of symmetry is obtained as follows:
x = -4/2 = -2.
For the fourth function, we have that:
a = -2, b = -8.
Hence:
x = -8/4 = -2.
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Work out the equation of the straight line
shown below.
Give your answer in the form y = mx + C,
where m and c are integers or fractions in
their simplest forms.
Y
6
5
4
3
2-
1
-6 -5 -4 -3 -2 -1 0
-14
-2-
-3+
-4-
-5-
-6-
1 2 3 4 5 6
X
Answers
Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.
What is a straight line?A straight line is made up of many points connected at each end. Any straight line's slope, m, is determined by the formula. The slope-intercept formulation of a linear equation is y = mx + b. The equation's variables are X and Y. The slope of the line (m) and the value of y when x is 0 are represented by the values m and b, respectively.
[tex]m = \frac{y2-y1}{x2 - x1}[/tex]
given
the graph is,(0,8) and (9,2)
The slope of the line is,
m = 1/2
Because it crosses the y-axis at the point where the intercept C is equal to 8,
The equation of the line will be :
⇒ y = mx + c
⇒ y = (1/2)x + (8)
⇒ y = x/2 + 8
Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.
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Why are 3 4 5 and 5 12 13 Pythagorean triples?
Answers
A Pythagorean triple is a set of three positive integers a, b, and c that satisfies the equation a2 + b2 = c2.
In this case, the triple is (3, 4, 5) and (5, 12, 13).
The equation for the first triple is 32 + 42 = 52.
3² = 9
4² = 16
9 + 16 = 25
25 = 25
The equation for the second triple is 52 + 122 = 132.
5² = 25
12² = 144
25 + 144 = 169
169 = 169
Therefore, both sets of numbers are Pythagorean triples because they both satisfy the equation a2 + b2 = c2.
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what are the properties of rational exponents and how are they used to solve problems
Answers
The properties of the rational exponents are given and a rational equation is of the form b = aˣ
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the rational exponent equation be A
Now , the properties of the exponent equations are
mᵃ×mᵇ = mᵃ⁺ᵇ
The powers of the exponents are added together
mᵃ / mᵇ = mᵃ⁻ᵇ
The powers of the exponents are subtracted together
( mᵃ )ᵇ = mᵃᵇ
The powers of the exponents are multiplied together
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
Any number raised to the power of 0 is 1
m⁻ᵃ = ( 1 / mᵃ )
Hence , the exponents are solved
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Which set of side lengths belong to a right triangle?
Answers
Answer:
10 cm, 6cm, 8cm
Step-by-step explanation:
Answer:
10 cm,6 cm,8 cm
Step-by-step explanation:
PLEASE HELP IM IN 4th grade
Answers
Answer:
30 feet
Step-by-step explanation:
a = l * w
Its a square so l and w are the same
x * x = 900
30 * 30 = 900
----------------
If you know about square roots
x = √900
x = 30
Answer:
1 ture
2 false
3 false
4 ture
Step-by-step explanation:
x + y = 3
Which of the following equations is equivalent to the given equation?
3x + 2y = 18
2x + 3y = 18
3x + 2y = 3
Answers
The equation equivalent to the equation x + y = 3 is 6x + 6y = 18.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x + y = 3
Multiply 6 on both sides.
6x + 6y = 18
Thus,
The equation that is equivalent is 6x + 6y = 18.
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Find the volume of the triangular pyramid.
A. 192 cubic inches
B. 128 cubic inches
C. 24 cubic inches
D. 64 cubic inches
Answers
Answer:
im pretty sure its d
Step-by-step explanation:
What is the inverse of +5?
Answers
The inverse of +5 as calculated is found to be +1 / 5.
To find the inverse of +5 we can simply reciprocate it and the result will be the required answer.
reciprocal of +5 = 1 / 5.
Therefore, the answer is 1 / 5.
The opposite or reciprocal of a number or term in math is known as it's inverse. There are two types of inverse in math, the additive inverse and the multiplicative inverse.
The multiplicative inverse of a number for any n is given as 1/n. It is also called as the reciprocal of a number and 1 is called the multiplicative identity. On the other hand subtraction is the inverse of addition.
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is this right?? this assignment is graded and no links!!
Answers
Find the surface area of a cylinder that has a radius of 5.5 m and a height of 15 m.
Answers
Answer:
the Total surface area is your answer. it is 708.4 meters squared.
Step-by-step explanation:
see answer above.
Please help
Find the value of x
Find the measure of the two marked angles
PLEASE ALSO FIND X
(Mathematics)
Answers
On solving the provided question, by properties of parallel lines we got to know that - 1 - A 2 - C 3 - B 4 - D
what is alternate exterior angles?When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.
Matches are -When two parallel lines cross one other, the horizontal line is divided into two angles. Interior angles develop between the parallel lines, whereas alternative outside angles develop outside the parallel lines.
1 - A
2 - C
3 - B
4 - D
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In the figure below, AB is a diameter of circle P.
What is the arc measure of minor arc AD in degrees?
Answers
Answer:
D
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Can someone please help?!!!!!!
Answers
5d = 30 i cant find the answer
Answers
Answer:
d=6
Step-by-step explanation:
divide 30 by 5 to get the value of d
Answer:
Hey again d = 6
Step-by-step explanation:
5 × 6 = 30 therefore d = 6 HOPE THAT HELPS!
3x-3y=-6
3x+y=10 use subtraction please help thank you
need an ordered pair
Answers
Answer:
x=2, y=4. (2, 4).
Step-by-step explanation:
3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.
-----------------------------
x-y=-2
3x+y=10
---------------
4x=8
x=8/4=2
2-y=-2
y=2-(-2)=2+2=4
rewrite in Y = MX +b form show your work -6x+2y=10
Answers
Answer:
answer y= 3x +5
Step-by-step explanation:
-6x+2y=10
we need to get y by itself so move the -6x to the other side
you get
2y=6x+10
divide everything by 2
2y/2=6x/2+10/2
y= 3x+5
2.) divide both sides by 2 to get y by itself.
for each meal, Jeffrey eats either toast, cereal, or pancakes. How many different ways can Jeffrey choose his three meals for the day? PLSS HELP ASAP RN!
Answers
Answer:
27
Step-by-step explanation:
Jeffrey has three choices for breakfast: toast, cereal, or pancakes. Then, he has three choices for lunch: toast, cereal, or pancakes. Finally, he has three choices for dinner: toast, cereal, or pancakes.
Putting these together, Jeffrey has 3 * 3 * 3 = 27 possible ways to select the three meals.
15. At what rate per cent of interest will a sum of money become 6 times itself in
15 years?
Answers
Answer:
The rate of interest will be 40%
Step-by-step explanation:
So first consider the principal to be x
Then the SI (Simple interest) will become six times of itself that is 6x
The time is 15 years
Rate = SI × 100 / P × T
Now put the values
Rate = 6 × x × 100 / x × 15
Then after simplifying the rate will come 40 %
50 points help me out
Answers
Answer:x=20
Step-by-step explanation: <2 and <3 must be equal, so set 3x-10 equal to x+30, once simplified you get x equal to 20.
Answer:
x = 20
Step-by-step explanation:
Angle 2 and 3 are alternate (interior) angles which means that they are equivalent to each other.
3x-10=x+30
-x -x
2x-10=30
+10 +10
2x=40
x=20
pls help me what is the equation for this graph pls get it right :)
Answers
Answer: Y= 1/8x -2
Step-by-step explanation:
Y = mx+ b
Slope = y2-y1/x2-x1 = -1+2 / 8-0 = 1/8
Initial Y-Value = -2
The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p= -1/7x+200. A) Find a model that expresses the revenue R as a function of x. (Remember, R= xp). R(x)=____ B) What is the domain of R? C) What is the revenue if 200 units are sold? D) What quantity maximizes revenue? What is maximum revenue? E) What price should the company charge to maximize revenue?
Answers
A) The model that expresses the revenue R as a function of x is R(X) = -1/7x + 200
B) The domain of R is (-∞, +∞)
C) If 200 units are sold, then the revenue is $228.57
D) The quantity that maximizes revenue is 200 and the maximum revenue is $228.57
E) The price should the company charge to maximize revenue $228.57
Here we have given the function that can be model that expresses the revenue R as a function of x is written as,
=> R(X) = -1/7x + 200
Here the domain value of R has take the value from negative infinity to positive infinity.
When we take the value of x as 200, then the revenues of the sold goods is calculated as,
=> R(200) = -1/7 (200) + 200
When we simplify this one then we get the value of R as
=> R = 28.57 + 200
=> R = 228.57
As per the given function the maximum number of units sold is written as 200, and the maximum revenue is written as 228.57
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Out of 30 students surveyed, 17 have a dog. based on these results, predict how many of the 300 students in the school have a dog?
Answers
1. Use the proportion 17/30 = x/300 to find the answer
2. Cross multiply
30x = 5100, which can also be written as 3x = 510 because they both have at least 1 zero and 0/0 cancels out.
3. Divide both sides by 3 to get the variable alone
X = 3x/3 = 510/3
4. Simplify
X = 170
a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help, explanation required
Answers
If you take 1- .75= .25 then you take 51 divide by .25 then you get the original price of 204. To check you answer you can take 204 x .75=153 then you take 204-153=51
Identifying Characteristics of an Exponential Function
Consider the function f(x) = (6). What is the value of the growth factor of the function?
02
06
O 18
Answers
Answer:
6
Step-by-step explanation:
The growth factor is the number that is raised to an exponent.
Answer: 6
At the opening session of the United States Supreme Court, each justice shakes hands with all the others. There are nine justices that sit on the Supreme Court. How many handshakes do they make during the opening session
Answers
According to probability, total number of handshakes will be 36.
How many handshakes are possible?Handshakes equal n * (n - 1)/2. This is the case because a handshake between two people is not counted twice and each of the n people can shake hands with n - 1 people (they wouldn't shake their own hand). Any number of people can be calculated using this formula.
The first person will need to shake eight (8) people's hands. Only seven (7) hands will need to be shook by the second person because the first handshake will not be repeated. Due to the same factors as mentioned above, only six (6) people will require a handshake from the third person. This continues until the final person has no one left to shake hands with because everyone has already done so.
The formula to calculate how many handshakes were exchanged is n = 8 + 7 + 6 +... + 1 = 36.
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6. If ON = x^2 - 10, LM = -2x + 5, NM = 3x + 21 and OL = 4y + 18, find the values of x and y
given that LMNO is a parallelogram.
(show work)
Answers
Given that ON = [tex]x^{2}[/tex] - 10; LM = -2x + 5; NM = 3x + 21; and OL = 4y + 18; with x and y values of [tex]\sqrt{10}[/tex] and -4.5, respectively.
What is the values of x and y ?ON = [tex]x^{2}[/tex] - 10 ⇒ [tex]x^2[/tex] = 10 ⇒ x =[tex]\sqrt{10}[/tex]
OL = 4y + 18 ⇒ 4y =-18 ⇒ y = -18/4 ⇒ -4.5 .
The issue at hand is here A parallelogram of O N M L is nm. Suppose ON = [tex]x^{2}[/tex] - 10 or LM = -2x + 5. Here, we must determine what X's value is. then look up N M N O L. Due to the parallelogram shape of ONA male, there are four.
Since N M is equal to the opposing sides of a parallelogram and an e parallelogram, we can express that as follows. due to the parallelogram's equal opposite sides. We can therefore write [tex]x^{2}[/tex] - 10 where N M = O L. that is four, -2x + 5, and. Change the two sides of the equation, then write four. Nine times X is equivalent to [tex]x^{2}[/tex] - 10.
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What is the volume of a rectangular prism with a length of 2 inches, a width of 1 inch, and a height of One-half inch?
One-half inches cubed
1 inch cubed
2 inches cubed
3 and one-half inches cubed
Answers
The volume of the rectangular prism is 1 inch.
Step-by-step explanation:
Volume is LxWxH so it would be
2 x 1 x 1/2
Which is 1
Answer:
1
Step-by-step explanation:
did it
Derek is cutting a piece of plywood into the shape of a triangle to use as part of a set for a school play. How should the triangle be classified? 50° 90° 40° O A. right, isosceles B. right, scalene C. acute, scalene о O D. obtuse, isosceles
Answers
Answer:
C.58.3
Step-by-step explanation:
Im pretty sure im right
6 and 18/54 simplified