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4 years ago

For what value of x does 64^3x = 512^2x+12

Mathematics

1 answer:

aleksandr82 [10.1K]4 years ago

3 0

Answer:

<h2>no solution</h2>

Step-by-step explanation:

$Use:\\\\(a^n)^m=a^{nm}\\--------------\\64=2^6\\512=2^9\\\\\text{therefore}\\\\64^{3x}=512^{2x+12}\\\\(2^6)^{3x}=(2^9)^{2x+12}\\\\2^{(6)(3x)}=2^{(9)(2x+12)}\iff6(3x)=9(2x+12)\\\\18x=9(2x+12)\qquad\text{divide both sides by 9}\\\\\dfrac{18x}{9}=\dfrac{9(2x+12)}{9}\\\\2x=2x+12\qquad\text{subtract 2x from both sides}\\2x-2x=2x-2x+12\\\\0=12\qquad\bold{FALSE}$

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Simplify (4xy^-2)/(12x^(-1/3)y^-5) and Show work ...?

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The answer is $\frac{x^{4/3}y^{3}}{3}$ .

The fraction is: $\frac{4xy^{-2} }{12 x^{-1/3} y^{-5} }$
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Since $\frac{x^{a} }{x^{b}} =x^{a-b}$ ,
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$\frac{4 }{12 }*\frac{x }{ x^{-1/3} }*\frac{y^{-2} }{ y^{-5} }= \frac{1*4}{3*4}* x^{4/3}*y^{3}= \frac{1}{3} * x^{4/3}*y^{3}= \frac{x^{4/3}y^{3}}{3}$

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3 years ago

The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches. What is the volume of the smaller cylinder?

zalisa [80]

Hey there :)

The volume formula of a cylinder is:
V = $\pi$ r²h

The volume of the larger volume is given to be 9648³ and the height is 18 in
We need to find the radius first

9648 = $\pi$ r²(18)
$\frac{9648}{18}$ = $\pi$ r²
536 = $\pi$ r²
$\frac{536}{ \pi}$ = r²
$\sqrt{ \frac{536}{ \pi } }$ = r
r ≈ 13.06

The ratio of the big cylinder to small cylinder is:
18 : 9 (given height)
So the big cylinder is 2 times bigger than the small cylinder
Therefore the radius of the big cylinder is as well 2 times bigger

$\frac{13.06}{2} = r$
r ≈ 6.53 ( the radius of the small radius )

V (of small cylinder) = $\pi$ (6.53)²(9)
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3 years ago

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Leni [432]

Answer:

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Step-by-step explanation:

X+Y=11

2X-Y=-5 by substitution Y=11-X

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so, y=5-2x

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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