All categories

3 years ago

The volume of a sphere is 972π ft3. What is the radius of the sphere? Use the formula V = 4 3 πr3 to find your answer.

Mathematics

2 answers:

djyliett [7]3 years ago

6 0

$972 \pi = \frac{4}{3} \pi r^{3}$
$729 = r^{3}$
$r = 9$

Ede4ka [16]3 years ago

5 0

Answer:

The radius of the sphere is 9 ft.

Step-by-step explanation:

Given : The volume of a sphere is 972π ft³.

To find : What is the radius of the sphere?

Solution :

The formula of volume of sphere is $V=\frac{4}{3}\pi r^3$

Where, Volume of the sphere is 972π ft³.

r is the radius of the sphere.

Substitute the value in the formula,

$972\pi=\frac{4}{3}\pi r^3$

$r^3=\frac{972\pi\times 3}{4\pi}$

$r^3=729$

$r=\sqrt[3]{729}$

$r=9$

Therefore, The radius of the sphere is 9 ft.

You might be interested in

5.6 x N= 2.24 N=? Please help

dlinn [17]

Answer:

N = -3.36

Step-by-step explanation:

5.6 x N= 2.24

-5.6 -5.6

N= -3.36

3 0

2 years ago

Read 2 more answers

2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0

2 years ago

Evaluate lim x→∞ (3x+1)^(4/x), using l'hospital's rule as needed. show all work using proper notation. as you show your work, if

Alborosie

$\displaystyle\lim_{x\to\inty}(3x+1)^{4/x}=\lim_{x\to\infty}e^{\ln(3x+1)^{4/x}}=e^{\lim\limits_{x\to\infty}\ln(3x+1)^{4/x}}$

$\displaystyle\lim_{x\to\infty}\ln(3x+1)^{4/x}=\lim_{x\to\infty}\frac{4\ln(3x+1)}x\stackrel{\mathrm{LHR}}=\lim_{x\to\infty}\frac{4\frac3{3x+1}}1=\lim_{x\to\infty}\frac{12}{3x+1}=0$

$\implies\displaystyle\lim_{x\to\infty}(3x+1)^{4/x}=e^0=1$

4 0

3 years ago

HELP!!!!!!!!!!!

Svetradugi [14.3K]

Using the mean concept, it is found that:

Relative to Sabrina's goal, her average swim time over the last five weeks is 0.1 hours.

-----------------------

The mean of a data-set is given by the <u>sum of all observations divided by the number of observations</u>.

In this problem:

The data-set is her swim time relative to her goal, which is: {1.25, -1, 2.25, 0, -2.}

5 observations.

Thus, the mean is:

$M = \frac{1.25 - 1 + 2.25 + 0 - 2}{5} = 0.1$

Relative to Sabrina's goal, her average swim time over the last five weeks is 0.1 hours.

A similar problem is given at brainly.com/question/24787716

7 0

2 years ago

I would appreciate if you answered!

anyanavicka [17]

Answer:

None of those options

Step-by-step explanation:

I just did the work myself and even ran it through a calculator but the correct answer isn't one of those options. Here's my work:

$-\frac{5}{6} =z+\frac{1}{8}\\-\frac{5}{8}-\frac{1}{8}=z\\-\frac{40}{48}-\frac{6}{48}=z\\-\frac{46}{48}=z\\-\frac{23}{24}$

I'd contact you teacher about that...it might be an error in their system (it's happened to me a few times before where the correct answer is marked as incorrect or isn't even an option)

8 0

2 years ago