Answer:
the model for the height, h, of the chair at a function of time is [tex]y = -20 \times sin (\frac{2\pi }{15} \times t + \frac{\pi }{2} ) + 26[/tex]
Step-by-step explanation:
To answer the question, we note that the height of the Ferris will varies proportionately to the angle of rotation, hence we can model the height according to he sine function as follows;
y = a·sin(b·x+c) + d
Where: a = Amplitude = Maximum displacement = r = 20 ft
or [tex]a = \frac{maximum - minimum}{2} = \frac{44 - 4}{2} = 20 \, ft[/tex]
The period, [tex]\frac{2\pi }{b}[/tex] = Time for one complete revolution, for a Ferris wheel making 4 revolutions per minute, we have
Period = 1 minute/4 = 15 seconds
Therefore, [tex]\frac{2\pi }{b}[/tex] = 15 seconds or [tex](b =\frac{2\pi }{15})[/tex]
d = the vertical shift is given by minimum + amplitude or maximum - amplitude = 6 + 20 = 26 ft
c = Phase shift since we want the chair to be at the minimum at t = 0 we put c = π/2
x = Independent variable, which in the case of the question is time, t
Therefore, the model for the height, h, of the chair at a function of time is as follows
[tex]y = -20 \times sin (\frac{2\pi }{15} \times t + \frac{\pi }{2} ) + 26[/tex]
i.e. y = -20×sin(2π/15 + π/2) + 26.
Final answer:
To model the height of the chair as a function of time on a Ferris wheel, use the equation h(t) = 20 × cos((8π/60)t) + 6, where t is in seconds and h(t) is in feet.
Explanation:
To write a model for the height, h, of the chair as a function of time, t, for a Ferris wheel with a radius of 20 feet and a rotation rate of 4 revolutions per minute, we must consider the motion of the wheel. Since the Ferris wheel completes one rotation in 15 seconds (60 seconds/4 minutes), the chair's height above the ground will depend on the cosine of the angular position of the chair. Including the initial condition of the chair being 6 feet above the ground at its lowest point, the mathematical model will be:
h(t) = 20 × cos(ωt + ϕ) + 6
where angular velocity ω is calculated from the rotation rate (4 revolutions per minute) and phase shift ϕ accounts for the initial position. Since t = 0 corresponds to the lowest point, ϕ is 0 degrees or 0 radians (cos(0) = 1). The angular velocity in radians per second is:
ω = 2π × rotation rate = 2π × 4 / 60 = 8π/60 rad/s
Thus, the final equation for the height of the chair as a function of time is:
h(t) = 20 × cos((8π/60)t) + 6
where t is in seconds and h(t) is in feet.
A hat contains four balls. The balls are numbered 3, 6, 6, and 7. One ball is randomly selected and not replaced, and then a second ball is selected. The numbers on the two balls are added together.
A fair decision is to be made about which of three sizes of ice cream cone will be ordered, using the sum of the numbers on the balls. The sizes are small, medium and large.
Which description accurately explains how a fair decision can be made in this situation?
If the sum is 9, a small cone will be ordered.
If the sum is 10 or 13, a medium cone will be ordered.
If the sum is 12, a large cone will be ordered.
If the sum is 9, a small cone will be ordered.
If the sum is 10 or 12, a medium cone will be ordered.
If the sum is 13, a large cone will be ordered.
If the sum is 9 or 10, a small cone will be ordered.
If the sum is 12, a medium cone will be ordered.
If the sum is 13, a large cone will be ordered.
If the sum is 9 or 12, a small cone will be ordered.
If the sum is 10, a medium cone will be ordered.
If the sum is 13, a large cone will be ordered.
Answer:
I believe the answer is B
Step-by-step explanation:
How long would it take a bus traveling at 52 km/h to travel 130 km ??
Answer: 2.5 hours
Step-by-step explanation:
130 / 52 = 2.5
A bus will take "2.5 hours" to travel.
Given that:
Speed of bus (s),
= 52 km/h
Distance (d),
= 130 km
As we know,
→ [tex]Speed = \frac{Distance}{Time}[/tex]
or,
→ [tex]Time = \frac{Distance }{Speed}[/tex]
By substituting the values, we get
[tex]=\frac{130}{52}[/tex]
[tex]=2.5 \ hours[/tex]
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In the right triangle shown, what is the value of x (to the nearest tenth)? (Picture shown above)
a. 9.1
b. 11.0
c. 21.4
d. 23.7
Answer:
i think it is c. good luck!!
Step-by-step explanation:
The value of x is 11.037
The correct option is (B)
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
Using Trigonometry,
cos 25 = B/ H
cos 25 = 10 / x
0.906 = 10/ x
x= 10/ 0.906
x= 11.037
Hence, the value of x is 11.037.
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Pls take a look at the picture! It should be easy if you know radicals.
Answer:
The answer is 2√15 .
Step-by-step explanation:
Using Indices Law :
[tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]
[tex] \sqrt{ - 6} \times \sqrt{ - 10} [/tex]
[tex] = \sqrt{ - 6 \times - 10} [/tex]
[tex] = \sqrt{60} [/tex]
Next, you have to find the common factors of 60 :
60 = 1×60
60 = 2×30
60 = 3×20
60 = 4×15
60 = 5×12
60 = 6×10
In order to simplify, we have to choose a perfect square from the factors above. In the factors above, 4 is a perfect square so that we can square root it :
[tex] \sqrt{60} [/tex]
[tex] = \sqrt{4 \times 15} [/tex]
[tex] = \sqrt{4} \times \sqrt{15} [/tex]
[tex] = 2 \times \sqrt{15} [/tex]
[tex] = 2 \sqrt{15} [/tex]
3 ratios that are equivalent to 3/8
Answer:
30/80 9/24 6/16
Step-by-step explanation:
Answer:
just multiply a fraction equal to 1 for example 2/2
3/8 x 2/2 = 6/16
3/8 x 3/3 = 9/24
3/8 x 4/4 = 12/32
it is equivalent because 2/2 is equal to 1 so it is being multiplied by 1
Step-by-step explanation:
A triangular prism. The rectangular sides are 6 centimeters by 10 centimeters, 10 centimeters by 5 centimeters, and 10 centimeters by 5 centimeters. The 2 triangular bases have a base of 6 centimeters and height of 4 centimeters. What is the surface area of the triangular prism shown? 32 square centimeters 120 square centimeters 184 square centimeters 1,560 square centimeters
Answer:
184
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
What is the inverse of function f?
f(x) = 10/9x+11
Answer:
hope this helps!
Step-by-step explanation:
The inverse function of the given function will be f(x)⁻¹ = ( 10 ) / ( 9x - 99).
What is an inverse function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. In an inverse function, the value of two variables x and y are interchanged, and then the value of y is given an inverse function.
Given function is f(x) = ( 10/9x) + 11. the inverse function will be calculated as below:-
y = 10/9x+11
x = ( 10 / 9y ) + 11
x - 11 = ( 10 / 9y )
9y / 10 = ( 1 / ( x - 11 )
9y = 10 / ( x - 11 )
y = ( 10 ) / ( 9x - 99 )
Therefore, the inverse function of the given function will be f(x)⁻¹ = ( 10 ) / ( 9x - 99).
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PLEASEEEEEE HELPPPP!!!!
What is the area of a circle with a radius of 6 inches? 9 pi inches squared 12 pi inches squared 36 pi inches squared 81 pi inches squared
Answer:
36π
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
BECAUSE U MULTIPLY THEN DIVIDE
The figure below is a net for a rectangular prism.
lb
Side a = 7 centimeters
Side b = 2 centimeters
Side c = 5 centimeters
What is the surface area of this figure?
Answer: which side is the length and which side is the height?
Simplify
12x^9
————
2x^3
o 6х3
o 6х6
o10х3
o10х6
Answer:
6 * x^6
Step-by-step explanation:
We have (12x^9) / (2x^3)
(12x^9) / (2x^3) = 6 * (x^9/x^3) Divide the constants first
(12x^9) / (2x^3) = 6 * x^ (9-3)
(12x^9) / (2x^3) = 6 * x^6
Express 8^1/2 in simplest radical form.
Final answer:
To express [tex]8^{1/2[/tex]in simplest radical form, recognize that it's equivalent to the square root of 8, then simplify to 2√2 by breaking down 8 into prime factors and finding pairs of factors.
Explanation:
To express [tex]8^{1/2[/tex] in simplest radical form, we follow these steps:
Recognize that an exponent of 1/2 is equivalent to the square root.
Find the square root of 8, which can also be written as √8.
Since 8 is not a perfect square, we can simplify it by breaking it down into its prime factors: 8 = 2 x 2 x 2.
Group the factors into pairs to determine the square root: 8 has one pair of 2s.
This pair comes out of the radical as a single 2, leaving one 2 inside the radical: 2√2.
Therefore, 8^1/2 simplifies to 2√2, which is the simplest radical form.
Use the divisibility tests to determine whether 900 is divisible by 2, 3, 5, 6, and 10
Answer:3
Step-by-step explanation:
13. In a week the prices of a bag of rice were 350,280,340,290,320, 310,300. The range is
A. 60
B. 70
C. 80
D. 100
so the right answer is 70.
Look at the attached picture ⤴
Hope it will help u
Answer:
B
Step-by-step explanation:
The range can be found by subtracting the lowest number from the highest number
First, arrange the numbers in order from least to greatest
350,280,340,290,320, 310,300
280, 290, 300, 310, 320, 340, 350
So, our lowest number is 280, and our highest is 350.
highest number - lowest number
Subtract 280 from 350
350-280
70
So, our range is 70, making B the correct answer
GIVING BRANLIEST
Which ordered pair is the solution to this system of equations?
y = 4
3x - 2y = 4
Group of answer choices
(0, 6)
(0, 4)
(-4, 4)
(4, 4)
Answer:
(4,4)
Step-by-step explanation:
Answer:
(4,4). You already know the y value is 4, so you just plug that into the second equation. You'd get 3x-8=4, then 3x=12, then x=4. (x,y)=(4,4)
help me answer this question
Answer:
a
Step-by-step explanation:
Answer: -8/5
Step-by-step explanation:
Joseph is ordering a taxi from an online taxi service. The taxi charges $4 just for the
pickup and then an additional $1 per mile driven. How much would a taxi ride code if
Joseph is riding for 9 miles? How much would a taxi ride cost that is m miles long?
Answer: $13 for the 9 mile ride.
The taxi ride that is m miles long would cost as follows: 4 + m
Step-by-step explanation:
The cost of Joseph's taxi ride is calculated by adding a flat fee of $4 to $1 for each mile driven. Thus, a 9-mile ride would cost $13. For a ride of m miles, the cost would be $4 plus $1 per mile.
Explanation:The cost of a taxi ride can be determined using a function that considers two components: a flat fee, and a rate per mile. In Joseph's case, the online tax service charges a $4 flat fee for pickup, and $1 per each mile driven. Hence, the equation for the cost of a taxi ride (C) for Joseph is as follows: C= 4+1*m.
For a ride of 9 miles, we would substitute m with 9: C = 4+ 1*9, which simplifies to C = $13. Therefore, a 9-mile ride would cost $13.
For a taxi ride that is m miles long, the cost would be C = 4 + 1*m. The 4 represents the flat fee, and the 1*m represents the cost per mile that is driven multiplied by the number of miles in the ride. Therefore, a taxi ride that is m miles long would cost $4 plus $1 per mile.
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Help looks like i forgot to read a ruler
Answer:
the second one
Step-by-step explanation:
Answer:
2nd one is right
Step-by-step explanation:
A bag contains 26 red marbles, 8 white marbles, and 5 gray marbles. You randomly pick out a marble, record its color, and put it back in the bag. You repeat this process 117 times. How many white or gray marbles do you expect to get?
Answer:
39
Step-by-step explanation:
What is the area of the rhombus?
square units
Answer:
Area = 80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Vertical length-16
Horizontal length- 10
make four separate triangles out of the rectangle
each triangle has an area of of 20 (8×5= 40 40/2=20)
multiply by 4
20×4=80
helpppppp! thank youuu
Answer:
three B
Step-by-step explanation:
simple addition
Define the Negative Exponent Property
Answer:
Dividing is the inverse (opposite) of Multiplying.
A negative exponent means how many times to divide by the number.
Answer:
There is a power property for negative exponent powers which says that a power with a negative exponent is equal to 1 between the same power, but with a positive exponent. In other words, to convert the exponent from negative to positive, the power is converted to the denominator
Step-by-step explanation:
two line are ___ if and only if they lie in the same plane and do not intersect, and two lines are __ if and only if they lie in the same plane and intersect at the right angles
A) partaken, perpendicular
B) perpendicular, bisectors
C) parallel, bisectors
D) perpendicular, parallel
the answer is C, I think because parallel lines never touch
The required answer is two lines are parallel if and only if they lie in the same plane and do not intersect, and two lines are perpendicular if and only if they lie in the same plane and intersect at the right angles. Option A is correct.
Given that,
An incomplete statement is given,
We have to complete the statement using the appropriate options that thinks fit to black space.
The line is a curve showing the shortest distance between 2 points.
Here,
Two lines are ___ if and only if they lie in the same plane and do not intersect.
The above statement is the definition of parallel lines, so the complete statement is,
Two lines are parallel if and only if they lie in the same plane and do not intersect.,
Two lines are __ if and only if they lie in the same plane and intersect at the right angles
The above statement is the definition of perpendicular,
So the complete statement is,
Two lines are perpendicular if and only if they lie in the same plane and intersect at the right angles.
Thus, the required correct option is option A, Parallel and perpendicular.
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79.99 - 12% + 8%
please dhow your work
thank you
And be safe
Answer:
79.95
Step-by-step explanation:
The first step is to rewrite the percentages into decimals so they can be added or subtracted easier. To turn a percentage into a decimal, remove the percent sign and move the decimal two spaces to the left (in other words, divide the number by 100).
12% becomes -0.12
8% becomes 0.08
Now, let's solve.
79.99 - 0.12 + 0.08
Evaluating 79.99 - 0.12, the equation becomes 79.87 + 0.08.
Evaluating 79.87 + 0.08, we get the final answer, 79.95.
A side length of a regular hexagon is 14 inches. What is the perimeter of the hexagon?
Answer:
84 inches
Step-by-step explanation:
A regular hexagon has 6 sides where all 6 sides are congruent meaning that each side is 14 inches.
Hence:
14*6=84
In Conclusion:
The perimeter of the hexagon is 84 inches.
Hope this helps!
Answer:
84
Step-by-step explanation:
14+14+14+14+14+14=84
A hexagon has 6 equal sides and you add all of the sides to find perimeter.
Find the area of the parallelogram shown below.
Answer:
The answer is 21
Step-by-step explanation:
The answer is 21 because...
It is hard to explain but for step one you need to take the dotted line and the shape above hat and move it underneath the other shape to make a perfect rectangle.Step two since the dotted line is our new bottom. It has a length of 7. In this step we multiply 3 times 7 Step 3 this is the final step in which 3 times 7 equals 21.Hope this helped :)A square mirror has an area of 25 square feet. How long is each edge of the mirror?
Answer:
5 feet
Step-by-step explanation:
5x5
thanks jimtompson5910 for helping me fix my mistake
Some number times itself is 25. The question is: which number?
That would be 5 since 5 times 5 = 25
You can also apply the square root to 25 to get 5, to avoid guessing and checking.
Simplify the expression:
-5a – 6a + -9a
Answer:
-20a
Step-by-step explanation:
-5a-6a+-9a
-11a+-9a
-20a
A scaled drawing uses a scale factor of 1:25. Is the drawing a reduction or an enlargement? Support your conclusion with an example.
Answer:
Reduction scale
Step-by-step explanation:
Enlarging scale means that the drawing is larger than the actual object. Hence the representative fraction will be greater than unity. For reducing scale the representative fraction is less than unity.
So now looking at 1:25, we see it's a reduction scaling because it's fraction is less than unity.
And what 1:25 means is that 1 on paper while the actual size of the object is 25
there’s also D
D: 4m on top and 4m on the side
Answer:
A and B.
Step-by-step explanation:
To find the area, you need to multiply the length and width.
A = L x W
5 x 4 = 20
10 x 2 = 20