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drek231 [11]
3 years ago
14

A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 3x. Find the height of t

he cone in terms of y.
Mathematics
1 answer:
timurjin [86]3 years ago
5 0
Vcyl = Vcone
pi×x^2×y = 1/3×pi×(3x)^2 (h)
pi's cancel--> x^2•y = 3x^2 (h)
h = y/3
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407 mi/h

Step-by-step explanation:

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Speed of plane (s) = 470 mi/h

Height of plane above radar station (h) = 1 mi

Let the distance of plane from station be 'D' at any time 't' and let 'x' be the horizontal distance traveled in time 't' by the plane.

Consider a right angled triangle representing the above scenario.

We can see that, the height 'h' remains fixed as the plane is flying horizontally.

Speed of the plane is nothing but the rate of change of horizontal distance of plane. So, s=\frac{dx}{dt}=470\ mi/h

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D^2=h^2+x^2\\\\D^2=1+x^2

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

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Now, plug in all the given values and solve for \frac{dD}{dt}. This gives,

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Therefore, the distance from the plane to the station is increasing at a rate of 407 mi/h.

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