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3 years ago

HELP PLEASE

Mathematics

1 answer:

Afina-wow [57]3 years ago

3 0

Answer:

6.08 ft

Step-by-step explanation:

Volume of cone = $\frac{1}{3}$ $\pi$ r²h

Radius = $\sqrt{ \frac{V}{\frac{1}{3}\pi h } }$

$R = \sqrt{\frac{376.8}{\frac{1}{3} \pi 10} }$

$R = \sqrt{\frac{376.8}{10.47} }$

$R = \sqrt{36.98}$

$R = 6.08$

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\int\limits^0_\pi {x*sin^{m} (x)} \, dx

Ket [755]

Let

$I(m) = \displaystyle \int_0^\pi x\sin^m(x)\,\mathrm dx$

Integrate by parts, taking

u = x ==> du = dx

dv = sinᵐ (x) dx ==> v = ∫ sinᵐ (x) dx

so that

$I(m) = \displaystyle uv\bigg|_{x=0}^{x=\pi} - \int_0^\pi v\,\mathrm du = -\int_0^\pi \sin^m(x)\,\mathrm dx$

There is a well-known power reduction formula for this integral. If you want to derive it for yourself, consider the cases where m is even or where m is odd.

If m is even, then m = 2k for some integer k, and we have

$\sin^m(x) = \sin^{2k}(x) = \left(\sin^2(x)\right)^k = \left(\dfrac{1-\cos(2x)}2\right)^k$

Expand the binomial, then use the half-angle identity

$\cos^2(x)=\dfrac{1+\cos(2x)}2$

as needed. The resulting integral can get messy for large m (or k).

If m is odd, then m = 2k + 1 for some integer k, and so

$\sin^m(x) = \sin(x)\sin^{2k}(x) = \sin(x)\left(\sin^2(x)\right)^k = \sin(x)\left(1-\cos^2(x)\right)^k$

and then substitute u = cos(x) and du = -sin(x) dx, so that

$I(2k+1) = \displaystyle -\int_0^\pi\sin(x)\left(1-\cos^2(x)\right)^k = \int_1^{-1}(1-u^2)^k\,\mathrm du = -\int_{-1}^1(1-u^2)^k\,\mathrm du$

Expand the binomial, and so on.

8 0

3 years ago

PLEASE HELP

mr Goodwill [35]

If 3 ft = 1yard

? = 16 yards?

Thats $\frac{16 yards * 3ft}{1yard}$

The common values cancel each other out and you'll have 48 feet :)

3 0

2 years ago

Is 0.09 greater than 0.7

chubhunter [2.5K]

No, 0.7 is greater than 0.09

0.70 > 0.09

hope this helps

3 0

4 years ago

Read 2 more answers

1/9,1/3,5/9 find the rule

anastassius [24]

It’s going up by 2/9 . if you did it for the first one it’d b 3/9 which is 1/3

3 0

3 years ago

What are the zero(s) of the function f(x)=4x2-36x over x-9?

vfiekz [6]

F(x) = (4x^2 - 36x) / (x-9)
0 = 4x * (x-9) / (x-9)
0 = 4x

x=0
hope this helps

7 0

3 years ago

Read 2 more answers