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2 years ago

The volume of a sphere is 2254 pi m^3 what is the surface area of the sphere to the nearest 10th

1 answer:

8 0

By definition. The volume of the sphere is:
V = (4/3) * (pi) * (r ^ 3)
Where,
r: radius of the sphere.
Substituting values:
2254 pi = (4/3) * (pi) * (r ^ 3)
Clearing the radio we have:
r ^ 3 = (3/4) * (2254)
r = ((3/4) * (2254)) ^ (1/3)
r = 11.91255883
Then, the surface area is:
A = 2 * pi * r ^ 2
Substituting values:
A = 2 * 3.14 * (11.91255883) ^ 2
A = 891.6 m ^ 2
Answer:
The surface area of the sphere is:
b. 891.6 m ^ 2

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2 years ago

If mLA = 15, then 3mLA = 45

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2 years ago

Is each fraction in simples form? Write yes or no 2/4

shusha [124]

Hey there! :D

When a fraction is still divisible by a number, then it is not in it's simplest form.

For example, 3/6.

I know for a fact that 6/3=2 <== 3 is also divisible by itself.

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1/2 <== simplest form.

Try the same with 2/4.

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2 years ago

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Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

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3 years ago

I need to solve for x, help please.

BaLLatris [955]

Answer:

x = 52 i hope this helps! :)

Step-by-step explanation:

so first you gotta realize that every triangle has an interior angle measurement sum of 180 degrees

so we are given 3 angles 74 degrees x + 2 and x

we now are going to put this into an equation 74 + x + 2 + x = 180

now lets combine like terms to get 76 + 2x = 180

then we are going to subtract the 76 from both sides 2x = 104

now lets divide both sides by 2 x = 52

so x = 52

we can plug in the value of x into both of the other equations to find the angle measurement

52 degrees

52 + 2 = 54 degrees

and then we have 74 degrees

add the 52, 54, and the 74 to make sure it is equal to 180 degrees

106 + 74 = 180

so yes, x does indeed equal 52 degrees

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3 years ago

Read 2 more answers