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3 years ago

A ratio of two numbers is equal to 3:8. If the smaller number is 12,find the greater number.

Mathematics

1 answer:

iragen [17]3 years ago

6 0

The other no. is:

32

As you can see that in the ratio given, 3 is the smaller no. and 12 too.

So when we divide 12 by 3, we get 4 

Then to find the other no. we need to multiply 4 with 8 (which is the other no. in the ratio given)

Therefore, we get the other no. as 32

And also when you divide 12 by 32,

You get the answer as 3 by 8 (which is the given ratio)

Hope you found this helpful!

THANK YOU!!

∝ Sidhdi

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2 years ago

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Answer:

The rate of change of the volume $\frac{dV}{dt}$ when the height is 9 centimeters and the radius is 6 centimeters is $24\pi \:\frac{cm^3}{s}$

Step-by-step explanation:

This is a related rate problem because you know a rate and want to find another rate that is related to it. If 2 variables both vary with respect to time and have a relation between them, we can express the rate of change of one in terms of the other.

From the information given we know:

$\frac{dr}{dt}=\frac{1}{2}\:\frac{cm}{s}$
$\frac{dh}{dt}=\frac{1}{2}\:\frac{cm}{s}$
The volume of a cone of radius r and height h is given by $V=\frac{1}{3} \pi r^2 h$

We want to find the rate of change of the volume $\frac{dV}{dt}$ when the height is 9 centimeters and the radius is 6 centimeters.

Applying implicit differentiation to the formula of the volume of a cone we get

$\frac{dV}{dt}=\frac{1}{3}\pi [r^2\frac{dh}{dt}+2rh\frac{dr}{dt} ]$

Substituting the values we know into the above formula:

$\frac{dV}{dt}=\frac{1}{3}\pi [(6)^2\frac{1}{2}+2(6)(9)\frac{1}{2} ]\\\\\frac{dV}{dt}=\frac{1}{3}\pi[18+54]\\\\\frac{dV}{dt}=\frac{72\pi}{3}=24\pi \:\frac{cm^3}{s}$