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4 years ago

Find the area of the regular polygon.

Mathematics

2 answers:

Shkiper50 [21]4 years ago

8 0

The height of the triangle is 5√3. The area is 1/2(base x height). The first choice is correct.

ollegr [7]4 years ago

4 0

Area of equilateral triangle = s²√3/4

A = 10 *10√3 / 4 = 25√3

A = 25√3

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3 years ago

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3 years ago

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm^3/s) when the diameter is 60

nexus9112 [7]

Answer:

The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere is given by the following equation:

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

In which r is the radius.

Implicit derivatives:

This question is solving by implicit derivatives. We derivate V and r, implicitly as function of t. So

$\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}$

The radius of a sphere is increasing at a rate of 4 mm/s.

This means that $\frac{dr}{dt} = 4$

How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm?

This is $\frac{dV}{dt}$ when $r = \frac{d}{2} = \frac{60}{2} = 30$ . So

$\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}$

$\frac{dV}{dt} = 4\pi*(30)^2*4$

$\frac{dV}{dt} = 1508$

The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.

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3 years ago