Question 7 (1 point) Sovle for x. x2 625

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 $\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi *15}{15}) = \frac{2}{3} \pi$ m/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 pickle jar deal has the best price per ounce? $3.45 or 14 oz $4.35 for 16 oz $3.29 for 12 oz $4.25 for 15 oz

Allisa [31]

To find the answer divide each money amount by the cost:
3.45/14=0.246428571429
4.35/16=0.271875
3.29/12=0.274166666667
4.25/15=0.283333333333
The pickle jar that has the best deal is 14 oz for $3.45

Hope this helps!

8 0

3 years ago

I need help drawing the graph of -2x+2y=-4

True [87]

Arrange in slope intercept form.....
2y = 2x -4
y = x - 2

So, the line would go up......crossing the y axis at -2.........hope this helps

4 0

3 years ago

Read 2 more answers

Three ways to make 26

Alik [6]

Answer:

13 times 2

52 divided by 2

20 plus 6

Step-by-step explanation:

6 0

3 years ago

Imagine the United States only had two postage stamps, a 3 cent stamp and a 7 cent stamp. If you can put any number of stamps on

cricket20 [7]

Answer:

not possible: 1, 2, 4, 5, 8, 11
possible: all others

Step-by-step explanation:

Obviously, all multiples of 3 and 7 can be paid.

1 cent can be added by adding a 7-cent stamp and taking away two 3-cent stamps. 2 cents can be added by adding three 3-cent stamps and taking away one 7-cent stamp. Hence any value more than 7 +2(3) = 13 cents can always be accommodated.

Amounts that are impossible:

1, 2, 4, 5, 8, 11 cents

All other positive integer amounts are possible.

7 0

3 years ago