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3 years ago

The formula for the volume sphere is V=4/3pie r^3 what is the formula solved for r?

Mathematics

2 answers:

oksian1 [2.3K]3 years ago

3 0

Answer:

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

Step-by-step explanation:

From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.

$V=\frac{4}{3} \pi r^{3}\\\\ \text{Multiplying both sides by 3/4 we get}\\\\\frac{3V}{4} = \pi r^{3}\\\\ \text{Dividing both sides by } \pi \\\\ \frac{3V}{4 \pi} = r^{3}\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{\frac{3V}{4 \pi}} = r$

Therefore:

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

juin [17]3 years ago

3 0

Answer:

The formula for radius of sphere is r = ∛(3V/4π)

r = (3V/4π)¹/³

Step-by-step explanation:

It is given formula for volume of sphere.

Volume of sphere = 4/3 πr³

Where r is the radius of sphere

<u>To find the radius r of sphere </u>

Volume V = 4/3 πr³

r³ = 3V/4π

r = ∛(3V/4π)

Therefore formula for radius of sphere is r = ∛(3V/4π)

r = (3V/4π)¹/³

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2 years ago

Read 2 more answers

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

Luden [163]

Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

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2 years ago

What is the value of x in the equation 3/2 (4X - 1) - 3x = 5/4 - (x +2)

Leokris [45]

Step-by-step explanation:

3/2(4x-1)-3x = 5/4-(x+2)

6x -3/2 -3x = 5/4 -x -2