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3 years ago

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Mathematics

2 answers:

kkurt [141]3 years ago

6 0

Answer:

410 1/2 inch cubes

Step-by-step explanation:

if 210 1/2 inch cubes can fit

then 410 is doubble of 210

drek231 [11]3 years ago

6 0

Answer: 240 quater inch cubes

Step-by-step explanation:

We know that the prism can fit 210 1/2 inch cubes. If we were to hypotheicly cut each block in half it would now have 240 1/4 inch cubes.

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3 years ago

Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.

Naya [18.7K]

Answer: $\boldsymbol{-25+18\sqrt{2}}$

The expression is in the form $a+b\sqrt{2}$ where a = -25 and b = 18

==========================================================

Work Shown:

Let $x = 3\sqrt{2}$ and then square both sides

$x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\$

We'll use both x and x^2 later on.

---------------------

The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

$\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\$

$\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}$

Therefore,

$\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}$

-------------------------------------

Checking the answer:

Use a calculator to find that,

$\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571$

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

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Read 2 more answers

In the arithmetic sequence, -12, -17, -22, -27... which term has a value of -68?

RSB [31]

Answer:

-68 is not a term in the given sequence