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DanielleElmas [232]
2 years ago
15

What is the value of the expression ? (243^2)^1/10 A.9 B.81 C.3 D.27

Mathematics
1 answer:
podryga [215]2 years ago
7 0

(243^2)^{\tfrac 1{10}}\\\\=243^{\tfrac 2{10}}\\\\=243^{\tfrac 15}\\\\=(3^5)^{\tfrac 15}\\\\=3^{\tfrac 55}\\\\=3^1\\ \\=3\\\\\text{Hence the the answer is C.}

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What is the value of p in the linear equation 24p + 12 – 18p = 10 + 2p – 6?
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HELP URGENT PLEASE
ki77a [65]

Answer:

A)

15 hours

B)

108 hours

C)

2074.29 miles

Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.

A)

In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;

(24/360) = (x/225)

solving for x;

x = (24/360) * 225 = 15 hours

B)

In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;

(24/2π radians) = (x/9π radians)

Solving for x;

x = (24/2π radians)*9π radians = 108 hours

C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

                         = 7920*3.142

                         = 24891.43 miles

Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;

(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

5 0
3 years ago
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