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3 years ago

Evaluate and simplify the following expression (b^2)^3

Mathematics

1 answer:

Ainat [17]3 years ago

3 0

Answer:

It finally equals to b^6.

Step-by-step explanation:

When you raise and exponent to the power of another exponent you multiply the exponents but keep the base(b) the same.
Therefore in this case (b^2)^3 equals to b^6.

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Every month, the plant grows another 6 cm. After two months

nignag [31]

Answer:

49 cm

Step-by-step explanation:

To find the height of the plant after 4 months, add 12 to 37, since the plant grows 6 cm each month:

37 + 12

= 49

So, after a total of 4 months, the plant will be 49 cm tall

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3 years ago

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Inessa [10]

Answer:

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Step-by-step explanation:

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3 years ago

What’s the LCM of 6 and 50

marin [14]

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4 years ago

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

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

Divide both sides by r

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

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

4 years ago

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To the nearest tenth, what is the distance between the point (10, -11) and (-1, -5)

Eva8 [605]

Answer:

The distance will be in centimeters

Step-by-step explanation:

You will do the multiply and subtract

5 0

3 years ago