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aleksklad [387]
3 years ago
5

Find the missing values of the variables

Mathematics
1 answer:
hodyreva [135]3 years ago
7 0

Answer:

What

Step-by-step explanation:

What is the missing variables

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Jamie is riding a Ferris wheel that takes fifteen seconds for each complete revolution. The diameter of the wheel is 10 meters a
Agata [3.3K]

Answer:

The answers to the question is

(a) Jamie is gaining altitude at 1.676 m/s

(b) Jamie rising most rapidly at t = 15 s

At a rate of 2.094 m/s.

Step-by-step explanation:

(a) The time to make one complete revolution = period T = 15 seconds

Here will be required to develop the periodic motion equation thus

One complete revolution = 2π,

therefore the  we have T = 2π/k = 15

Therefore k = 2π/15

The diameter = radius of the wheel = (diameter of wheel)/2 = 5

also we note that the center of the wheel is 6 m above ground

We write our equation in the form

y = 5*sin(\frac{2*\pi*t}{15} )+6

When Jamie is 9 meters above the ground and rising we have

9 = 5*sin(\frac{2*\pi*t}{15} )+6 or 3/5 = sin(\frac{2*\pi*t}{15} ) = 0.6

which gives sin⁻¹(0.6) = 0.643 =\frac{2*\pi*t}{15}

from where t = 1.536 s

Therefore Jamie is gaining altitude at

\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) = 1.676 m/s.

(b) Jamie is rising most rapidly when   the velocity curve is at the highest point, that is where the slope is zero

Therefore we differentiate the equation for the velocity again to get

\frac{d^2y}{dx^2} = -5*(\frac{\pi *2}{15} )^2*sin(\frac{2\pi t}{15}) =0, π, 2π

Therefore -sin(\frac{2\pi t}{15} ) = 0 whereby t = 0 or

\frac{2\pi t}{15} = π and t =  7.5 s, at 2·π t = 15 s

Plugging the value of t into the velocity equation we have

\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) = - 2/3π m/s which is decreasing

so we try at t = 15 s and we have \frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi *15}{15}) = \frac{2}{3} \pim/s

Hence Jamie is rising most rapidly at t = 15 s

The maximum rate of Jamie's rise is 2/3π m/s or 2.094 m/s.

7 0
3 years ago
What is the volume of the cylinder below?
snow_lady [41]

Volume of cylinder = πr²h

Volume = π (12)² × 17

= 2448 π units³

Thus the answer is (d)

4 0
3 years ago
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Andrew jogs for 3 miles each day on the weekdays and for 6.5 miles each day over the weekend. What is the average distance that
kirill [66]
Set up the data:
3,3,3,3,3,6.5,6.5
15+13=28
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He runs an average of 4 miles a day
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Which is equivalent to (-2ab^3) (-3a^2b^5)
Artemon [7]

Answer:

6 a^3 b^8

Hope That Helps!


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PLease tell me the inequalities and the answers also label which problems you d. I was out sick and I have no idea what to do lo
tatuchka [14]

Answer:

1) Amy can invite 17 people.

2) x > 76

3) 40 - 6 is greater than or equal to 3x

4) x is greater than or equal to 98

Step-by-step explanation:

1) 50 + 8x = 200

2) 200 < 3x - 28

3) 40 = 6 +3x

4) (95 + 78 + 89 + x)/4 is greater than or equal to 90

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2 years ago
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