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3 years ago

The radius r of a sphere is 6 units. Find the volume of the sphere. Write your answer in terms of . The volume is cubic units.

Mathematics

1 answer:

kirza4 [7]3 years ago

8 0

Answer:

The formula used to calculate the sphere radius is: r = ∛((3/4) · V / π) Symbols. r = Sphere radius; V = Sphere volume; π = Pi = 3.14159… Volume of Sphere. Enter the volume contained within a sphere. Radius of Sphere. This is the radius of a sphere that corresponds to the specified volume.

Step-by-step explanation:

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Reggie can line a football field in 120 minutes. Rosalinda can line a football field in 80 minutes. If they work together, how m

wel

Answer:

48 minutes

Step-by-step explanation:

Given that;

Rosalinda can line the football field in 80 minutes

Reggie can line the football field in 120 minutes

Lets assume that if they work together, they will take T minutes to line the football field

Hence;

Thus in 1 minute, Rosalina can line 1/80 of the field where as Reggie can line 1/120 of the field

$\frac{1}{T} =\frac{1}{120} +\frac{1}{80} \\\\\frac{1}{T} =\frac{2+3}{240}\\\\$

The sum of the two fractions will represent the size of the field that can be lined in 1 minute.

$\frac{1}{T} =\frac{5}{240} \\\\\frac{1}{T} =\frac{1}{48} \\T= 48$

The reciprocal of the sum of the two fractions will represent the time taken for both Rosalinda and Reggie to line the field.

Answer ; It will take them 48 minutes for them to line the football field

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Step-by-step explanation:

abc = 1

We have to prove that,

$\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1$

We take left hand side of the given equation and solve it,

$\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}$

Since, abc = 1,

$\frac{1}{c}=ab$ and c = $\frac{1}{ab}$

By substituting these values in the expression,

$\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}$