Emily is on a Ferris wheel and her height is modeled by the equation
27
y = 30.48 cos2pi/4.25 (x - 2) + 34.27 where x = the number of minutes since the
ride began and y = the height in feet of Emily.
a) What is the radius of the Ferris wheel?
b) How long does it take Emily to make one rotation?
The radius is______
feet and it takes Emily_____
minutes for one rotation.

Emily Is On A Ferris Wheel And Her Height Is Modeled By The Equation27y = 30.48 Cos2pi/4.25 (x - 2) +

Answers

Answer 1

The given function for the height of the Ferris wheel is a sinusoidal equation.

a) The radius is 30.48 feet and it takes Emily 4.25 minutes for one rotation

Reasons:

The function that gives the height of the Ferris wheel is presented as follows;

[tex]\displaystyle y = 30.48 \cdot cos \frac{2\cdot \pi }{4.25} \cdot \left(x - 2 \right) + 34.27[/tex]

Where;

x = The number of minutes since the ride began

y = The height in feet of Emily

a) Required:

The radius of the Ferris wheel

Solution:

Comparing the given equation with the general equation of a Ferris wheel, we have;

[tex]\displaystyle f(t) = \mathbf{A \cdot trig\left(B \cdot \left(t + C\right) \right) + D}[/tex]

The amplitude of the Ferris wheel = A = 30.48

The amplitude, A = The largest distance from the center = The radius, r

A = r

Therefore;

The radius of the Ferris wheel, r = A = 30.48 feet

b) The time it takes the Emily to make one rotation is given by the period, T, of the motion of the Ferris wheel as follows;

[tex]\displaystyle T = \mathbf{\frac{2 \cdot \pi}{B}}[/tex]

By comparison, we have;

[tex]\displaystyle B = \frac{2 \cdot \pi}{4.25}[/tex]

Therefore;

[tex]\displaystyle The \ period, \, T = \frac{2 \cdot \pi}{\left(\frac{2 \cdot \pi}{4.25} \right)} = 4.25[/tex]

The time it takes Emily to make one rotation, T = 4.25 minutes

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How much force is required to accelerate a 4 kg mass at 6 m/s2

Answers

Answer:

is it 24 N?

as we know ....

force=mass * acceleration

force=4kg*6m/s2

hence force is 24N

The required Force = 24 N

What is Force?

The push or pull on an object with mass causes it to change its velocity.

Given that a body of 4 kg mass is accelerated at 6 m/s²

Force = ma

where m = mass and a = acceleration

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Answer:

1/15

Step-by-step explanation:

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Step-by-step explanation:

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Question 5 of 10
Which of the following rational functions is graphed below?
10 H
10
10
O A. F(x) =
FIX) *-*
X5
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Answers

We want to find the equation for the graphed rational function. Notice that the options are not given, so I will try to find the function only from the graph.

The function is:

[tex]f(x) = \frac{(x - 5)}{x - 1}[/tex]

How to analyze the graph of a rational function?

The first thing that we can see in the graph is that we have vertical asymptotes at x = 1.

The one in the positive side (of the x range) goes to negative infinity, while the other goes to positive infinity, then the equation will be something like:

[tex]f(x) = \frac{something}{x - 1}[/tex]

Such that the asymptotes are caused when the denominator is equal to zero.

We can see that we also have a horizontal asymptote at y = 1.

This means that, as x tends to infinity, our function will tend to 1, so we have something like:

[tex]f(x) = \frac{(x + b)}{x - 1}[/tex]

The horizontal asymptote is equal to the ratio of the leading coefficients when both polynomials have the same degree, like here, so we can take the two leading coefficients equal to 1, such that:

y = 1/1 = 1

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[tex]f(0) = \frac{b}{-1} = -b[/tex]

And if you look at the graph, you can see that at x = 0 we have:

f(0) = 5

then b = -5

So the function is:

[tex]f(x) = \frac{(x - 5)}{x - 1}[/tex]

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Round any answers to the nearest tenth if necessary.
ad
Technology required. Find the
missing measurements.
nd
35
А.
21
B
BC is 40
I
units, degrees, and 60
degrees.

Answers

He’s gonna give u a link he did it to me and it didn’t work

help me due today it is mathematics

Answers

Answer:

Miranda is correct because the value 7 makes the equation equal

I am not sure what goes in the blanks, those are my best guesses.

Step-by-step explanation:

34 = 27 + p

7 = p

Hopefully this helps!

Brainliest please?

solve using quadratic formula
3n^2-2n-5=0

Answers

=5/3   =−1

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

If x = 5-2√6, find the value of:
(i) x + 1/x
(ii) x² + 1/x²
Please solve ASAP​

Answers

Answer:

x+(1/x) = 10 and x²+ (1/x²) = 98

Step-by-step explanation:

Given that :

x = 5-2√6

1/x = 1/(5-2√6)

The denominator = 5-2√6

The Rationalising factor of 5-2√6 = 5+2√6

On Rationalising the denominator then

⇛ 1/x = [1/(5-2√6)]×[(5+2√6)/5+2√6)]

⇛ 1/x = (5+2√6)/[5-2√6)(5+2√6)]

⇛ 1/x = (5+2√6)/[5²-(2√6)²]

Since (a+b)(a-b) = a²-b²

Where ,

a = 5 and b = 2√6

⇛1/x = (5+2√6)/(25-24)

⇛ 1/x = (5+2√6)/1

⇛ 1/x = 5+2√6

Now,

x +(1/x)

⇛ 5-2√6+5+2√6

⇛ 5+5

⇛ 10

Therefore, x+(1/x) = 10.

On squaring both sides then

⇛ [x+(1/x)]² = 10²

⇛ x²+2(x)(1/x)+(1/x)² =100

⇛ x²+2+(1/x)² = 100

⇛ x²+(1/x²) = 100-2

⇛ x²+(1/x²) = 98

Therefore, x²+(1/x²) = 98.

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

16.9 minus 13 equals to 3.9 increase

Answer:

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Repost
A group of tourists are on a three-day hiking trip. They hike ⅛ of the trail on the first day. On the second day, they hike 4/7 of the remaining distance. On the third day, they hike 1/3 of the remaining distance, plus the final 8 km. How many kilometers long is the trail?

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Answers

Answer:

13/12=37

Step-by-step explanation:

e/kaid_274404147475337871026587/assig!
Khan Academy
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Of the 50 U.S. states, 4 have names that start with the letter W.
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Answer:

Step-by-step explanation:

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The answer to the first box would be 4

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Answers

Answer:

6 hours.

Step-by-step explanation:

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Answer:

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Answers

Answer:

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Answers

Answer:

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Answers

Answer:

Option A

Step-by-step explanation:

-(12 x 2) x (-6) = -12 x (2 x b)

=> -24 x -6 = -12 x 2b

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=> b = -6

Hoped this helped.

1.Amulya is x years now. Write expressions for her age 5 years ago?

Take Sarita’s Age to be y years
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b) What was her age 3 years now?
c) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
d)Grandmother is 2 years younger than grandfather. What is his grandmother ’s age?
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Answer:

Step-by-step explanation:

1)    a = x - 5

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Answers

$320,000 is what the company produces with 8000 units.-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Are the ratios 6:1 and 19:3 equivalent?

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Answer: no<3

Step-by-step explanation:

leave a thanks if helped plz

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Answers

Answer:

Body surface area is calculated a) in m2 from weight and height.

Step-by-step explanation:

Basically the surface has to be in m2, because you have two dimensions when you multiply: e.g. when you have a lawn 10m x 10m, then you multiply 10 times 10, and meters times meters, so

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Mort and George are 18 miles apart on a path when they start moving toward each other. Mort runs at a constant speed of 7 miles per hour, and George walks at a constant speed of 5 miles per hour. How long does it take until Mort and George meet?

Answers

Answer:

  1 1/2 hours

Step-by-step explanation:

In one hour, the distance between them is reduced by 7+5 = 12 miles. At that rate, the 18 mile distance between them will be reduced to zero in ...

  time = distance/speed

  time = (18 mi)/(12 mi/h) = 3/2 h

It will take 1 1/2 hours until Mort and George meet.

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Answers

[tex]\\ \sf\longmapsto \dfrac{9}{24}=\dfrac{3}{x}[/tex]

[tex]\\ \sf\longmapsto \dfrac{3}{8}=\dfrac{3}{x}[/tex]

[tex]\\ \sf\longmapsto 3x=24[/tex]

[tex]\\ \sf\longmapsto x=24/3[/tex]

[tex]\\ \sf\longmapsto x=8[/tex]

13. A stack of lumber contains the following: three 1" x 6" X 8' pieces of yellow pine. six 2" x 10" x 12' pieces of redwood. six 1" x 8" 10' pieces of fir. How many total board feet of lumber are in this stack? *


180 board ft

162 board ft

192 board ft

172 board ft

Answers

Answer:

Step-by-step explanation:

A board foot is 1 inch thick by 1 ft by 1 ft

(3) 1 x 6  8'  are already 1 inch thick ½ ft wide and 8 ft long

  3 x 1 x (6/12) x 8 = 12 board ft.

(6) 2" x 10" x 12'  are 2 thick x 10/12 ft wide by 12 ft long

  6 x 2 x (10/12) x 12 = 120 board ft.

(6)  1" x 8" x 10'

  6 x 1 x (8/12) x 10 = 40 board ft

12 + 120 + 40 = 172 board ft

Is ( - 1, 2) a solution of the system y > x and x + y > 0?
O No, because ( - 1, 2) is a solution to only one of these inequalities.
O Yes, because ( – 1, 2) is a solution to both inequalities.
O Yes, because ( - 1, 2) is the point of intersection of the two boundary lines of this system.
No, because ( – 1, 2) is not a solution to either inequality.

Answers

Answer:

Yes, because (-1,2) is a solution to both inequalities

Step-by-step explanation:

2>-1 so the first inequality is correct

-1+2>0 so the second inequality is correct

What determines whether a relationship
is proportional or not?

Answers

Answer:

When two ratios exhibit the same connection, they are said to be proportionate. Two ratios may be tested for proportionality by writing them as fractions and then reducing them to the smallest possible number. In this case, your ratios are proportionate since the reduced fractions are the same.

Step-by-step explanation:

Hope it helps:)


Logan is a great babysitter. He makes $9 an hour. Jeanette is an even better babysitter. She makes $16 an hour. Jeanette works 18 hours each week. How many
hours does Logan need to work in order to earn as much money as Jeanette earns in a week?

Answers

Answer:

18hx16money=288 dollars

Step-by-step explanation:

to ez and np

Answer:

32 hours a week

Step-by-step explanation:

First you have to find out how much Jeanette makes. You can do this by multiplying 16 x 18 since she makes $16 18 times a week. This gives you $288 that she makes each week.

Now to find how much Logan would have to work you take 288 and divide it by 9. You do this because you need to see how many times 9 goes into 288 to give you the amount of hours. When you divide you get 32.

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