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3 years ago

I need help simplifying this

Mathematics

1 answer:

faust18 [17]3 years ago

3 0

Answer:

n^2

Step-by-step explanation:

cancel the common factor between n^7 and n^2

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Please change the numbers to the best-estimated value within each division problem:

sammy [17]

Answer:

27.9 (rounded, actual answer 27.909090, repeating)

3.7 (rounded, actual answer 3.70174672489)

6.7 (rounded, actual answer 6.67408231368)

Step-by-step explanation:

Divide

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4 years ago

Tayler has $320 to pay for dining room chairs. She expects to pay about $80 per chair. Her friend told her that she has 33 that

Kryger [21]

320/80 = 4
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4 years ago

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3 years ago

What is the antiderivative of sin^2(x)cos^2(x)?

marin [14]

Answer:

$\frac{x}{8}-\frac{\sin(4x)}{32}+C$

Step-by-step explanation:

[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]

Recall that we can express the squared trig functions in terms of cos(2x). That is,

$\cos(2x)=2\cos^2x-1 \\ \cos(2x)=1 - 2\sin^2x.$

And so inverting these,

$\cos^2x=\frac{1}{2} (1+\cos2x) \\ \sin^2x=\frac{1}{2} (1-\cos2x)$ .

Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).

$\sin^2x \cdot \cos^2x =\frac{1}{2} (1-\cos2x) \cdot \frac{1}{2} (1+\cos2x) = \frac{1}{4}(1-\cos^2(2x)).$

Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).

$\cos(2x)=2\cos^2x-1 \Rightarrow \cos(4x)=2\cos^2(2x)-1 \Rightarrow \cos^2(2x) = \frac{1}{2}(1+\cos(4x))$

So then,

$\sin^2x \cdot \cos^2x = \frac{1}{4}(1-\cos^2(2x)) = \frac{1}{4}(1-\frac{1}{2}(1+\cos(4x))) = \frac{1}{4}(1-\frac{1}{2}-\frac{1}{2}\cos(4x))=\frac{1}{8}(1-\cos(4x)).$

This is now integrable (phew),

$\int \sin^2x\cos^2x \ dx = \int \frac{1}{8}(1-\cos(4x)) \ dx = \frac{1}{8} \int (1-\cos(4x)) \ dx = \frac{1}{8}(x-\frac{1}{4}\sin(4x))+C.$

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3 years ago

A volume of a sphere is 792\7cm cube find its surface area

olga_2 [115]

Answer: The answer is 113.14 $cm^{2}$ . The detailed answer is given below:

Step-by-step explanation:

volume of sphere = $4/3 \pi r^{3}$ ∴ where radius = r

= $792/7$

now, we find r.

$4/3 \pi r^{3}$ = $792/7$

⇒ $\pi r^{3}$ = 792/7 x 3/4 ( bring 3/4 to RHS )

⇒ $r^{3}$ = 594/7 x 7/22 ( bring $\pi$ to RHS )

⇒ $r^{3}$ = 27

⇒r = $\sqrt{27}$

⇒r = 3 _(1)

surface area of sphere = $4\pi r^{2}$

= 4 x 22/7 x $3^{2}$ ( from _(1) )

= 113.14 $cm^{2}$

4 0

3 years ago