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babymother [125]

3 years ago

11

How do I solve this equation????

1 answer:

Alexus [3.1K]3 years ago

4 0

So for this question (for finding x and y) you will want to use elimination. To do this you will need to bring the x and y to the same side (I put them on the left):
-3/2x+y=6
x+y=0
Now subtract the y on the bottom from the top to isolate x:
3/2x=6
Now the easiest way to bring over the 3/2 to isolate the x fully is to convert it to decimal (1.5) and divide it by 6 (because when multiplication on one side of problem the only way to bring it over is to divide):
x=6/1.5
which simplifies to:
x=4
Hope this helps!

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or

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Step-by-step explanation:

Given

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Required

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Rotating about the x-axis.

Using the washer method to calculate the volume, we have:

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$v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx$

Evaluate the exponents

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Simplify like terms

$v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx$

Factor out 8

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Integrate

$v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0$

$v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0$

Substitute 2 and 0 for x, respectively

$v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])$

$v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])$

$v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ]$

$v = 8\pi [ \frac{16}{3} - \frac{16}{4} ]$

Take LCM

$v = 8\pi [ \frac{16*4- 16 * 3}{12}]$

$v = 8\pi [ \frac{64- 48}{12}]$

$v = 8\pi * \frac{16}{12}$

Simplify

$v = 8\pi * \frac{4}{3}$

$v = \frac{32\pi}{3}$

or

$v=\frac{32}{3} * \frac{22}{7}$

$v=\frac{32*22}{3*7}$

$v=\frac{704}{21}$

$v=33.52$

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