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BigorU [14]
2 years ago
6

you have a 20 ounce bottle of juice. you pour out 1/4 of the bottle to share with a friend. if your our out 3 ounces for yoursel

f, what fraction of the 20 ounces will be left in the bottle?
Mathematics
1 answer:
seropon [69]2 years ago
5 0
12 ounces will be left in the bottle

Turn the 1/4 into a decimal which is 0.25 and times that by 20 and you’ll get 5, 5 is the amount of ounces you poured for your friend. Subtract 20 ounces by 5 ounces and you’ll get 15 ounces, then subtract 15 by 3 which is the amount of juice you poured for yourself and you’ll be left with 12 ounces in the bottle.
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Step-by-step explanation:

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Answer:

22670.8 cm³/min

Step-by-step explanation:

Given:

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Rate of growth of radius is, \frac{dr}{dt}=5\ cm/min

The rate at which the air is pumped in the balloon can be calculated by finding the rate of increase in the volume of the balloon.

So, first we find the volume of the sphere in terms of 'r'. As the balloon is spherical in shape, the volume of the balloon is equal to the volume of a sphere. Therefore,

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

Now, rate of increase of volume is obtained by differentiating both sides of the equation with respect to time 't'.

Differentiating both sides with respect to time 't', we get:

\frac{dV}{dt}=\frac{d}{dt}(\frac{4}{3}\pi r^3)\\\\\frac{dV}{dt}=\frac{4\pi}{3}(3r^2)(\frac{dr}{dt})\\\\\frac{dV}{dt}=4\pi r^2(\frac{dr}{dt})

Now, plug in 19 cm for 'r', 5 cm per minute for \frac{dr}{dt} and solve for \frac{dV}{dt}. This gives,

\frac{dV}{dt}=4\pi (19 cm)^2(5\ cm/min)\\\\\frac{dV}{dt}=4\times 3.14\times 361\times 5\ cm^3/min\\\\\frac{dV}{dt}=22670.8\ cm^3/min

Therefore, the rate at which the air is being pumped into the balloon is 22670.8 cm³/min.

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