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xenn [34]
3 years ago
9

How to complete this

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
8 0

Answer:

4x^{6}y^{7}

Step-by-step explanation:

Using the rule of exponents

a^{m} × a^{n} = a^{(m+n)}

12x^{5} × y^{3} × \frac{1}{2}x x \frac{2}{3}y^{4}

= 12 × \frac{1}{2} × \frac{2}{3} × x^{(5+1)} × y^{(3+4)}

= 4x^{6}y^{7}


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3 years ago
A.) The formula for the volume of a sphere is given below and the relationship between the radius r and the diameter d is r=d/2.
Tasya [4]

Answer:

\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3

Step-by-step explanation:

<u>The Volume of a Sphere </u>

The volume of a sphere of radius r is given by:

\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3

A. )

If the diameter of the sphere is d, the radius is r=d/2. Substituting:

\displaystyle V=\frac{4}{3}\cdot \pi\cdot \left (\frac{d}{2}  \right )^3

Operating

\displaystyle V=\frac{4}{3}\cdot \pi\cdot \frac{d^3}{8}

Simplifying

\displaystyle V=\frac{1}{6}\cdot \pi\cdot d^3

B.)

The diameter of the sphere is 2/3 cm, thus the volume is:

\displaystyle V=\frac{1}{6}\cdot \pi\cdot \left (\frac{2}{3}  \right )^3

Operating:

\displaystyle V=\frac{1}{6}\cdot \pi\cdot \frac{8}{27}

\displaystyle V=\frac{8}{27}\frac{1}{6}\cdot \pi

\boxed{\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3}

8 0
3 years ago
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