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2 years ago

The pyramid shown has a height of 14 inches and a base area of 60 in2. Find the volume of the pyramid.

Mathematics

1 answer:

Kamila [148]2 years ago

8 0

Volume of pyramid is $280 in^{3}$ .

The pyramid has a height 14 inches and a base area of 60 in2.

What is volume?

Volume is a three - dimensional quantity that is used to measure the capacity of a solid shape.

Volume of the pyramid = $Area base$ X $\frac{height}{3}$

= $60.\frac{14}{3}$

= $280$ $in^{3}$

So the volume of pyramid = $280$ $in^{3}$

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We can assume that the decline in the population is an exponential decay.

An exponential decay can be written as:

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Where A is the initial population, b is the base and t is the variable, in this case, number of hours.

We know that: A = 800,000.

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And we know that after 6 hours, the popuation was 500,000:

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then we have that:

b^6 = 500,000/800,000 = 5/8

b = (5/8)^(1/6) = 0.925

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P(t) = 800,000*0.925^t

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4 years ago

The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the

Leona [35]

Answer:

The first number is 16

The second number is 6

The third number is 64

Step-by-step explanation:

The information from the word problem are;

The count of the numbers in the sum = 3 numbers

The value of the sum of the three numbers = 86

The value of the third number = 4 × The value of the first number

The value of the first number = 10 + The value of the second

Let 'x' represent the first number, let 'y' represent the second number and let 'z' represent the third number, we have;

x + y + z = 86...(1)

z = 4 × x...(2)

x = y + 10...(3)

From equation (3), we get;

x = y + 10

∴ y = x - 10...(4)

Substituting the value of <em>z</em> from equation (2) and the value of <em>y</em> from equation (4) in equation (1) gives;

x + y + z = 86

z = 4 × x = 4·x

y = x - 10

∴ x + y + z = x + (x - 10) + 4·x = 86

x + (x - 10) + 4·x = x + x - 10 + 4·x = 6·x - 10 = 86

6·x = 86 + 10 = 96

∴ x = 96/6 = 16

x = 16

From equation (2), we get;

z = 4 × x

∴ z = 4 × 16 = 64

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From equation (4), we get

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