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steposvetlana [31]
3 years ago
13

The volumes of two similar cones are 36π cm3 and 288π cm3. The base radius of the smaller cone is 3 cm. Calculate the base radiu

s of the larger cone.
Mathematics
1 answer:
Jlenok [28]3 years ago
6 0
V_1=36\pi\ cm^3\\\\V_2=288\pi\ cm^3\\\\\frac{V_2}{V_1}=k^3\ \ \ (k-similar\ scale)\\\\k^3=\frac{288\pi}{36\pi}\\\\k^3=8\\\\k=\sqrt[3]8\\\\k=2

the\ base\ radius\ of\ the\ smaller\ cone\ is\ 3cm\\\\the\ base\ radius\ of\ the\ bigger\ cone\ i\ 2\cdot3cm=6cm
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You got the equations correct, great job on that!

Let "s" be the variable that represents how many shirts were bought. Let "p" represent the total price/cost.

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Equation for the store in Arlington:

p = 120 + 2.5s (120 is base cost, and cost increases 2.5 per shirt)

We want to find a point where the systems are equal; thus, we are solving for a system of linear equations, and we already have the equations we need.

p = 80 + 3.5s

p = 120 + 2.5s

We know that variable "p" is equal for both equations; thus, we can combine both equations into:

80 + 3.5s = 120 + 2.5s

Subtract both sides by 2.5s

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Subtract both sides by 80

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Thus, both equations are equal when 40 shirts are bought.

To find the cost, use any of the two equations (or both) to find the total cost, which should be equal.

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Thus, the total price/cost at both stores is $220.

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