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podryga [215]
2 years ago
15

Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is i

ncreasing when the diameter of the balloon is 20 cm
Mathematics
1 answer:
Romashka-Z-Leto [24]2 years ago
3 0

0.08 cm/min

Step-by-step explanation:

Given:

\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}

Find \frac{dr}{dt} when diameter D = 20 cm.

We know that the volume of a sphere is given by

V = \dfrac{4\pi}{3}r^3

Taking the time derivative of V, we get

\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}

Solving for \frac{dr}{dt}, we get

\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})

\:\:\:\:\:\:\:= 0.08\:\text{cm/min}

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Find an equation of a line that goes through the points (1,6) and (4, -2). Write your answer in the form y=mx + y.
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Answer:

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Step-by-step explanation:

Moving from (1,6) to (4, -2) involves an increase of 3 in x and a decrease of 8 in y.  Thus, the slope of the line thru these two points is m = rise / run = -8/3.

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2 years ago
Admission to a home and garden show cost $7 per person during the week and $9 per person on the weekend. During one week of the
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For b) you already have two possibilities, since you have the intercepts. 
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<span>Solve for y: y= (-7/9)x + 15834 </span>

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<span>If you want more reasonable answers, let x= 9000 </span>
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