2 years ago

The side length, s, of a cube is 4x^2+3. If V=s^3, what is the volume of the cube?

Mathematics

1 answer:

sweet [91]2 years ago

7 0

The volume of the cube is $(4x^{2} +3)(4x^{2} +3)(4x^{2} +3)$ .

To simplify this, use the FOIL method between the first two terms, and then the product and the last term:

$(4x^{2} +3)(4x^{2} +3)(4x^{2} +3)\\(16x^{4}+12x^{2} +12x^{2} +9)(4x^{2} +3)\\(16x^{4}+24x^{2} +9)(4x^{2} +3)\\(64x^{6}+48x^{4} +96x^{4}+72x^{2} +36x^{2}+27)\\ 64x^{6}+144x^{4}+108x^{2} +27$

The answer is the first choice.

Hope this helps!!

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Rewrite the expression as a single power with a negative exponent

goblinko [34]

$~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \left(\cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3}\cdot \cfrac{1}{3} \right)^2\implies \left[ \left( \cfrac{1}{3} \right)^4 \right]^2\implies \left( \cfrac{1^4}{3^4} \right)^2 \\\\\\ \left( \cfrac{1^{4\cdot 2}}{3^{4\cdot 2}} \right) \implies \cfrac{1}{3^8} \implies 3^{-8}$

let's recall that

$\begin{array}{llll} 1^1&=&1\\ 1^{10}&=&1\\ 1^{1,000}&=&1\\ 1^{1,000,000,000}&=&1\\ 1^{1,000,000,000,000}&=&1\\ \end{array}$

8 0

1 year ago

A farm produces an average of 17.1 liters of milk per day. About how many days will it take to produce 200 liters of milk? A. ab

Aleks04 [339]

Average produce milk per day 17.1 liters
to produce 200 liters should be:

17.1x = 200
x = 200/17.1
x = 11,69

it close to 12. the answer is a. about 12 days

hope this help

6 0

3 years ago

Read 2 more answers

You randomly select one card from a 52-card deck. Find the probability of selecting a two or a five.

Vladimir79 [104]

Answer:

2/13

Step-by-step explanation:

there are 4 5s and 4 2s so

8/52

simplified is 2/13

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