Question

Sorry to bother but i need help

Answer 1

A rectangular pyramid has a base area of \[\frac{ x^2 +3x-10}{ 2x }\] square centimeters and a height of \[\frac{ x^2 -3x}{ x^2 -5x+6} \] centimeters. Write a rational expression to describe thw volume of the rectangular pyramid

Answer 2

volume = base * height so you would multiply the two equations

now, the hard part is to factor

do you know how you would factor x^2 + 3x - 10?

Answer 3

*actually it's (1/3)base*height sorry

Answer 4

how am i supposed to factor x^2 +3x -10?

Answer 5

first you would pick two integers that:

add up to 3
and
multiply to get -10

can you think of two integers that satisfy these requirements?

Answer 6

-5 and 2 or is it 5 and -2?

Answer 7

the sum has to be 3, so which pair would it be?

Answer 8

5 -2

Answer 9

good, so we take the positive 5, negative 2, and write our factors as

(x+5)(x-2)

now, we keep going for x^2 - 3x, do you see any common factors you can factor out?

Answer 10

x

Answer 11

good, so we factor that to get x(x-3)

now, the last thing, we can factor x^2 - 5x + 6, using the same method from before, pick two numbers that multiply to 6 and add up to -5

Answer 12

1 and -6

Answer 13

that's a good try but not quite, 1 * (-6) = -6 not positive 6

as a hint both the numbers need to be negative

Answer 14

oh ok thanks @Vocaloid

Answer 15

so you should get -2 and -3, thus we can re-write x^2 - 5x + 6 as

(x-2)(x-3)

then we go back to the expression

volume = (1/3)bh, now we substitute our factored forms, then cross out what we can:

Answer 16

see anything you can cross out from the num or denominator?

Answer 17

x-2

Answer 18

good, but there's two more things you can cross out

Answer 19

x-3

Answer 20

good, one more, it's a little harder to see

Answer 21

x?

Answer 22

good, so let's start crossing them out

Answer 23

only (x+5)/6 is left so that's your solution

Answer 24

ok thank you @Vocaloid