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elena55 [62]
2 years ago
14

Please help on the half circle one

Mathematics
1 answer:
yan [13]2 years ago
5 0

Answer:

28.26

Step-by-step explanation:

Area of a circle is pi * radius squared

The diameter is 6, so the radius is 3

pi * 3^2 = 3.14 * 9 = 28.26

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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
Which expression is equivalent to 12 + 24 p. A 2(6+24p) B 3(9+21p) C 4(3×6p) D 6 (2+3p)
Iteru [2.4K]

Answer:

C

Step-by-step explanation:

A. 2*6 = 12 but 24p*2 doesn't equal 24p

B. 3*9 doesn't equal 12, and 3*21p doesn't equal 24p

C. 4*3 equals 12 and4*6p=24p

D. 6*2=12, but 6*3p doesn't equal 24p

I hope this helps!!!

6 0
2 years ago
Read 2 more answers
The crowd at a music concert is estimated to be 14,000 people. The exact attendance is 10,528 people. What is the percent error?
Dmitriy789 [7]

Answer:

32.9%

Step-by-step explanation:

14,000-10,528=3,472

3,472/10,528=0.32978723

Idk what your supposed to round to, but I put 32.9%

6 0
3 years ago
Plz help asap.. I have no idea how to do this.
kondor19780726 [428]

Answer:

286

Step-by-step explanation:

Use term formula for +/-

Tn = a + (n-1)d

n= number of term

a= first number in sequence

d= difference between each number

T55 = 16 + (55-1)5

T55 = 16 + 270

=286

6 0
2 years ago
Read 2 more answers
Solve for x 5x2-4x=6
azamat

Answer:

1

Step-by-step explanation:

5x2 is 10 subtract that and add it to 6 which gives you -4 then you do -4/-4 which is 1

6 0
3 years ago
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