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3 years ago

Please help Please help The side length of a cube is 6 cm. What is the volume of the cube?

Mathematics

2 answers:

Readme [11.4K]3 years ago

7 0

The formula for the volume of a cube is V=S^3, where S is the length of the side.

Replace S with 6 to get V = 6^3.

6^3 is the same as 6 x 6 x 6.

6 x 6 = 36

36 x 6 = 216

The volume of the cube is 216 cubic cm.

uysha [10]3 years ago

5 0

Answer:

your answer is 216 cm

Step-by-step explanation:

multiply your side length by 36 since its a cube.

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3 years ago

If you invest $500 at 4% interest,compounded annually,how much is in the account at the end of six years?

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So, we'll find out how much interest this person will have in 6 years and then add it to the original deposit. To do this we will multiply all the factors:

500 x 0.04 x 6 = 120.
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3 years ago

In a competitive examination negative marks of 2 are awarded for each wrong answers and 4 marks for every correct answer. If nee

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Rajan gets 6 marks more

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3 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$