Answered: Find the area of the region described…

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Find the area of the region described in the following The region bounded by y = 24 Vx and y = 3x?

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter9: Systems Of Linear Equations

Section9.1: The Graphing Method

Problem 24WE

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Question

Find the
area of the region described in the following
The region bounded by y = 24 Vx and y
= 3x?

Expert Solution

Step 1

Given,

$y = 24 \sqrt{x} & y = 3 x^{2}$

To find limits of x we have,

$y = 24 \sqrt{x} = 3 x^{2} \Rightarrow 24 \sqrt{x} = 3 x^{2} \Rightarrow 8 \sqrt{x} = x^{2}$

Now squaring on the both sides,

$\Rightarrow 64 x = x^{4} \Rightarrow x^{4} - 64 x = 0 \Rightarrow x (x^{3} - 64) = 0 \Rightarrow x = 0 o r (x^{3} - 64) = 0 \Rightarrow x = 0 o r x = 4$

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