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egoroff_w [7]
3 years ago
5

Find the samllest value of K when : 280k is a perfect square 882 is a cube

Mathematics
1 answer:
adoni [48]3 years ago
5 0
280 = 7 x 2^3 x 5
882 = 7^2 x 2 x 3^2

For 280k to be perfect square , their powers need to be even
For 882 to be a cube, their powers need to be in multiple of 3,

To satisfy both parties,
K = 7 x 2^5 x 3^4 x 5^3 = 2268000
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HELP PLEASE!! I DONT UNDERSTAND!!!!!!!!!! THANKS SO MUCH
8090 [49]

Hello, please consider the following.

We will multiply the numerator and denominator by

4+\sqrt{6x}

to get rid of the root in the denominator.

First of all, we cannot divide by 0, right? So, we need to make sure that the denominator is different from 0.

4-\sqrt{6x} =0\sqrt{6x}=4\\\\\text{Take the square}\\\\6x=4^2=16\\\\x=\dfrac{16}{6}=\dfrac{8}{3}

We need to take any x real number different from 8/3 then and simplify the expression.

Let's do it!

\begin{aligned}\dfrac{4}{4-\sqrt{6x}}&=\dfrac{4(4+\sqrt{6x})}{(4+\sqrt{6x})(4-\sqrt{6x})}\\\\&=\dfrac{4(4+\sqrt{6x})}{(4^2-\sqrt{6x}^2)}\\\\&=\dfrac{4(4+\sqrt{6x})}{(16-6x)}\\\\&=\dfrac{2(4+\sqrt{6x})}{(8-3x)}\\\\&\large \boxed{=\dfrac{8+2\sqrt{6x}}{8-3x}}\end{aligned}

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8 0
3 years ago
last Friday,Adam had $22.33.over the weekend,he received some money for shoveling he neighbor's driveway.he now has $32.How much
crimeas [40]
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7 0
3 years ago
A helicopter blade does 3206 full turns in 7 minutes. Work out the number of full turns per minute? Then work out how many turns
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Step-by-step explanation:

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6 0
2 years ago
If f(x)=ln(sin(2x)), f''(π/4) is equal to​
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Use the chain rule to compute the second derivative:

f(x)=\ln(\sin(2x))

The first derivative is

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f'(x)=2\cot(2x)

Then the second derivative is

f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'

f''(x)=-4\csc^2(2x)

Then plug in π/4 for <em>x</em> :

f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4

4 0
3 years ago
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defon

Answer:

mutually exclusive

Step-by-step explanation:

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