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Leto [7]
3 years ago
15

PLEASE SHOW WORK

Mathematics
1 answer:
CaHeK987 [17]3 years ago
7 0

(C)

Step-by-step explanation:

The volume of the conical pile is given by

V = \dfrac{\pi}{3}r^2h

Taking the derivative of V with respect to time, we get

\dfrac{dV}{dt} = \dfrac{\pi}{3}\dfrac{d}{dt}(r^2h)

\:\:\:\:\:\:\:= \dfrac{\pi}{3}\left(2rh\dfrac{dr}{dt} + r^2\dfrac{dh}{dt}\right)

Since r is always equal to h, we can set

\dfrac{dr}{dt} = \dfrac{dh}{dt}

so that our expression for dV/dt becomes

\dfrac{dV}{dt} = \dfrac{\pi}{3}\left(3r^2\dfrac{dh}{dt}\right)

\:\:\:\:\:\:\:= \pi r^2\dfrac{dh}{dt}

Solving for dh/dt, we get

\dfrac{dh}{dt} = \dfrac{1}{\pi r^2}\dfrac{dV}{dt}

\:\:\:\:\:\:\:= \dfrac{1}{9\pi\:\text{m}^2}(36\:\text{m}^3\text{/s})

\:\:\:\:\:\:\:= \dfrac{4}{\pi}\:\text{m/s}

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3. Paula commutes 60 km each day for work, five days a week, nine months of the year. She travels 720
bezimeni [28]

Answer:

16,080 km.

Step-by-step explanation:

We want the total number of kilometers in one year.

so

4 weeks /month.

for Work:   9 months in the year  60 km/day  5 days/week

Family Visit :  720 km for 4 times a year

Personal:  200 km / month

Work total = 60 km/day * 5 days/week * 4week/month * 9 months

WorkTotal= 60*5*4*9 = 10,800 km

FamilyTotal= 4*720 = 2880 km

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7 0
3 years ago
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jonny [76]
It’s easier if you turn the fractions into decimals and arrange them in order from biggest to smallest. 3/4= 0.75, 5/6= 0.83, 7/9= 0.77, 1/2= 0.5, 2/3= 0.66, 7/12= .583, 15/24= 0.625. Then obviously, you order them from biggest to smallest:
0.83 (5/6), 0.77 (7/9), 0.75 (3/4), 0.66 (2/3), 0.583 (7/12), 0.5 (1/2).
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2 years ago
Find sin(2x), cos(2x), and tan(2x) from the given information.<br> tan(x) = − 1/2 , cos(x) &gt; 0
vodomira [7]

Answer:

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  • cos(2x) = 3/5
  • tan(2x) = -4/3

Step-by-step explanation:

It may be easiest to start with tan(2x).

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Then cosine can be found from ...

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Sine can be found from these two:

  sin(2x) = cos(2x)tan(2x) = (3/5)(-4/3)

  sin(2x) = -4/5

5 0
3 years ago
Lainey is sliding down a water slide that is 420 feet long at a rate of 42 feet per second. How long will it take Lainey to trav
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Answer:

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Step-by-step explanation:

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It took Lainey 10 seconds.

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3 years ago
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