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sweet-ann [11.9K]
3 years ago
9

How many time greater is 46 than 0.46?

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
5 0
46 is 100 times greater than 0.46. This is because 0.46 * 100 = 46, and 46/100 = 0.46. Hope this helps! :)
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The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi
storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

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To differentiate the product,

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\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)

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\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]

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\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}

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Then,

\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]

Now,

From the question

\frac{dr}{dt} = 7 m/min

\frac{dV}{dt} = 236 m^{3}/min

At the instant when r = 99 m

and V = 180 m^{3}

We will determine the value of h, using

V = \frac{1}{3}\pi r^{2}h

180 = \frac{1}{3}\pi (99)^{2}h

180 \times 3 = 9801\pi h

h =\frac{540}{9801\pi }

h =\frac{20}{363\pi }

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236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]

236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]

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708 = 30790.75 \frac{dh}{dt} + 76.36

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631.64 = 30790.75\frac{dh}{dt}

\frac{dh}{dt}= \frac{631.64}{30790.75}

\frac{dh}{dt} = 0.021 m/min

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Answer:

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Step-by-step explanation:

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