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sergiy2304 [10]
3 years ago
5

The radius of a sphere whose volume is 12 π cubic cm is??

Mathematics
2 answers:
dimaraw [331]3 years ago
8 0

Given a radius r, the volume of a sphere is given by

V=\dfrac{4}{3}\pi r^3

We can solve this formula for the radius, given the volume:

r=\sqrt[3]{\dfrac{3V}{4\pi}}

We can plug our value for the volume to get the radius:

r=\sqrt[3]{\dfrac{3\cdot 12\pi}{4\pi}}=\sqrt[3]{9}

Fiesta28 [93]3 years ago
7 0

Answer:

\sqrt[3]{9} or approximately 2.08 cm

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

12 pi = 4/3 pi r^3

Divide each side by pi

12 = 4/3 r^3

Multiply each side by 3/4

12 *3/4 = 3/4 * 4/3 r^3

9 = r^3

Take the cube root of each side

9 ^ 1/3 = r^3 ^ 1/3

9 ^ 1/3 = r

The radius is the cube root of 9

or approximately 2.080083823

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A prairie dog left its burrow 5 feet underground and started digging deeper into the ground. It digs straight down at a constant
SpyIntel [72]

Building and solving an equation to model the situation, it is found that it takes 4 min for the prairie dog to reach 13 feet underground.

  • Initially, the dog is 5 feet underground.
  • Each minute, the dog goes 2 more feet underground.

Hence, the underground height of the dog after t seconds is given by:

h(t) = 5 + 2t

The time it takes for the dog to reach 13 feet underground is <u>t for which h(t) = 13</u>, hence:

h(t) = 5 + 2t

13 = 5 + 2t

2t = 8

t = \frac{8}{2}

t = 4

It takes 4 min for the prairie dog to reach 13 feet underground.

A similar problem is given at brainly.com/question/25290003

7 0
2 years ago
A window in the shape of a rectangle as shown below has a width of x+5 and a length of x^2- 3x+7 express the area of the rectang
Ksju [112]

Answer:

x^3+x^2-5x+28

Step-by-step explanation:

since a=lw, the area is (x^2-3x+7)(x+4)

1. distribute parentheses \left(x^2-3x+7\right)\left(x+4\right)=x^2x+x^2\cdot \:4+\left(-3x\right)x+\left(-3x\right)\cdot \:4+7x+7\cdot \:4

2. apply +(-a)=-a rule x^2x+4x^2-3xx-3\cdot \:4x+7x+7\cdot \:4

3. Simplify

    Steps to simplify:

x^2x=x^3

3xx=3x^2

3\cdot \:4x=12x

7\cdot \:4=28

x^3+4x^2-3x^2-12x+7x+28

4. Add like terms =x^3+4x^2-3x^2-5x+28

5. Add like terms =x^3+x^2-5x+28

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2 years ago
Equation of the line that passes through the points (-3,8) and has a slope of zero
stiks02 [169]

Answer:

no

Step-by-step explanation:

6 0
3 years ago
Consider the polynomial equation x(x -3)(x +6)(x -7)=0. Which of the following are zeros of the equation? Select all that apply.
grigory [225]
(0,0), (3,0), (-6,0), and (7,0)
4 0
3 years ago
If you can solve it.Thanks in advance
vivado [14]

Answer:

f(g(x))=\frac{1}{(x^{2}+1)^{2}} +\sqrt[3]{x^{2}+1}

Step-by-step explanation:

we have

f(x)=x^{2} +\frac{1}{\sqrt[3]{x}}

g(x)=\frac{1}{x^{2}+1}

we know that

In the function

f(g(x))

The variable of the function f is now the function g(x)

substitute

f(g(x))=(\frac{1}{x^{2}+1})^{2} +\frac{1}{\sqrt[3]{(\frac{1}{x^{2}+1})}}

f(g(x))=\frac{1}{(x^{2}+1)^{2}} +\sqrt[3]{x^{2}+1}

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3 years ago
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