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adell [148]
2 years ago
5

What is the volume of the metal in this heavy-duty pipe? (It is not drawn to scale and the inside of the pipe is empty space.) S

how all work and be sure to label your answer. Use 3.14 to estimate pi.

Mathematics
1 answer:
Jlenok [28]2 years ago
6 0
The volume of the pipe is about 282.6 cubic feet.

First, we need to find the area of each circular cross section and subtract them to find the width of the pipe. The area of a circle is pi(r^2).

pi(3^2) - pi(2^2)
28.26 - 12.56 = 15.7

The width of the pipe is 15.7. Now, multiply that by 18 to find the volume.
15.7 x 18 = 282.6
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Given that (x+y+z)(xy+xz+yz)=18 and that x^2(y+z)+y^2(x+z)+z^2(x+y)=6 for real numbers x, y, and z, what is the value of xyz?
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Step-by-step explanation:

(x+y+z)(xy+xz+yz)=18 Equation 1

x^2(y+z)+y^2(x+z)+z^2(x+y)=6 Equation 2

What is the value of xyz where each variable represents a real number?

Let's expand equation 1:

(x+y+z)(xy+xz+yz)=18

x(xy)+x(xz)+x(yz)+y(xy)+y(xz)+y(yz)+z(xy)+z(xz)+z(yz)=18

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See if we can factor a little to get some of the left hand side of equation 2:

The first two terms have x^2 and if I factored x^2 from first two terms I would have x^2(y+z) which is the first term of left hand side of equation 2.

So let's see what happens if we gather the terms together that have the same variable squared together.

x^2y+x^2z+y^2x+y^2z+z^2y+z^2x+xyz+xyz+xyz=18

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x^2(y+z)+y^2(x+z)+z^2(y+x)+xyz+xyz+xyz=18

Replace the sum of those first three terms with what it equals which is 6 from the equation 2:

6+xyz+xyz+xyz=18

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