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2 years ago

What is 24tenths÷8

Mathematics

1 answer:

Taya2010 [7]2 years ago

7 0

Answer:

.03

Step-by-step explanation:

The answer would be .03 as you are dividing .24 by 8, which would be 3 if there was no decimal point. Though, .24 is two places past the ones place so the answer would have to be two places past the ones place. If you divide it, 8 can't go into 2, so you would put a 0 above it. Though, 8 can go into 24 three times, so you would put three. Therefore, your answer would be .03 as it is two places past the ones place and if it is multiplied by 8, it would make .24, or 24 tenths.

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bearhunter [10]

Answer:

$\frac{dh}{dt}=-\frac{1}{2\pi}cm/min$

Step-by-step explanation:

From similar triangles, see diagram in attachment

$\frac{r}{4}=\frac{h}{16}$

We solve for $r$ to obtain,

$r=\frac{h}{4}$

The formula for calculating the volume of a cone is

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

We substitute the value of $r=\frac{h}{4}$ to obtain,

$V=\frac{1}{3}\pi (\frac{h}{4})^2h$

This implies that,

$V=\frac{1}{48}\pi h^3$

We now differentiate both sides with respect to $t$ to get,

$\frac{dV}{dt}=\frac{\pi}{16}h^2 \frac{dh}{dt}$

We were given that water is drained out of the tank at a rate of $2cm^3/min$

This implies that $\frac{dV}{dt}=-2cm^3/min$ .

Since we want to determine the rate at which the depth of the water is changing at the instance when the water in the tank is 8cm deep, it means $h=8cm$ .

We substitute this values to obtain,

$-2=\frac{\pi}{16}(8)^2 \frac{dh}{dt}$

$\Rightarrow -2=4\pi \frac{dh}{dt}$

$\Rightarrow -1=2\pi \frac{dh}{dt}$

$\frac{dh}{dt}=-\frac{1}{2\pi}$

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