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3 years ago

7

earth's radius is approximately 4000 mi. about two thirds of the Earth's surface is covered by water. estimate the land area on

earth

1 answer:

UkoKoshka [18]3 years ago

7 0

9514 1404 393

Answer:

67 million square miles

Step-by-step explanation:

The area of a sphere is given by ...

A = 4πr²

So the area of the Earth is approximately ...

A = 4π(4000 mi)² ≈ 2.01×10^8 mi²

The area of the 1/3 that is not covered by water is approximately ...

(2.01×10^2 mi²)/3 = 6.7×10^7 mi²

The land area is estimated to be about 67 million square miles.

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What is the value of the x variable in the solution to the following system of equations?

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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

What is the slope of this graph?

sammy [17]

Answer:

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Step-by-step explanation:

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3 years ago

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A man finds that the angle of elevationof a building is 22º. After walking 20 m towards the building, he finds that the angle of

tensa zangetsu [6.8K]

Answer:

<em>The height of the building is 21.38 m</em>

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.

It's required to find the height of the building H.

The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:

$\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 22^\circ=\frac{H}{D+B}$

Multiplying by D+B:

$\tan 22^\circ(D+B)=H$

Dividing by tan 22°

$\displaystyle D+B=\frac{H}{\tan 22^\circ}$

Subtracting B:

$\displaystyle D=\frac{H}{\tan 22^\circ}-B\qquad\qquad[1]$

Applying to the smaller triangle:

$\displaystyle \tan 33^\circ=\frac{H}{D}$

Multiplying by D:

$\tan 33^\circ D=H$

Substituting from [1]:

$\displaystyle \tan 33^\circ \left(\frac{H}{\tan 22^\circ}-B\right)=H$

Substituting values:

$\displaystyle 0.6494 \left(\frac{H}{0.4040}-20\right)=H$

Operating:

$1.6074H-12.988=H$

$1.6074H-H=12.988$

$0.6074H=12.988$

$H = 12.988/0.6074$

H = 21.38 m

The height of the building is 21.38 m

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3 years ago