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olganol [36]
2 years ago
9

Find the volume of a pyramid with a square base, where the perimeter of the base is 13.4 in and the height of the pyramid is 7.6

in. Round your answer to the nearest tenth of a cubic inch.
Mathematics
1 answer:
VashaNatasha [74]2 years ago
7 0

Answer:

28.4in³

Step-by-step explanation:

Volume of the square based pyramid = L²H/3 where;

L is the length of a side of the square base

H is the height of the prism

Given

Perimeter of the base = 13.4 in

Height of the pyramid = 7.6in

First we need to get the length of the square base

Perimeter of a square = 4L

13.4 = 4L

L = 13.4/4

L = 3.35 in

Next is to find the required volume of the pyramid

V = L²H/3

V =  3.35²(7.6)/3

V = 85.291/3

V =  28.4 in³

Hence the volume of the pyramid to nearest tenth is 28.4in³

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Answer:

She should add 72 ml of the 20%-acidic solution and 48 ml of the 45%-acidic solution.

Step-by-step explanation:

Hi there!

The volume of the final solution will be the sum of the volume of each solution:

let x be the volume of the solution that is 20% acidic and y the volume of the solution that is 45% acidic. Then:

x + y = 120 ml

The amount of acid (let´s call it acidity units) of the total solution will be the sum of the amount of acid of each solution. If the final solution has 30 acidity units in 100 ml, then in 120 ml there will be (120 ml · 30 acidity units / 100 ml) 36 acidity units (concentration times volume over 100). Then the sum of the acidity units can be expressed as follows:

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0.2x + 0.45 y = 36

The solution of the system will be the pair (x,y) that satisfies both equations.

Let´s take the first equation and solve it for y:

x + y = 120 ml

subtract x to both sides of the equation

y = 120 - x

Now replace y in the second equation:

0.2x + 0.45 y = 36

0.2x + 0.45(120 - x) = 36

Apply distributive property

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subtract 54 to both sides of the equation

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divide both sides of the equation by -0.25

x = -18/-0.25

x = 72

Now, let´s calculate y:

y = 120 - x

y = 120 - 72

y = 48

She should add 72 ml of the 20%-acidic solution and 48 ml of the 45%-acidic solution.

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