Question

A builder wants to build a sump to store water in an apartment. He planned in such a way that its base dimensions are (x + 1) and (x-2).
Find how much he has to dig so that the volume of the rectangular prism will be
f(x) = x + 2x - 4x2 7x-2.​

Answer 1

Answer:

Step-by-step explanation:

V(x) = x³ + x²- 4x-4

base dimensions are (x + 1) and (x-2).

base area = (x + 1)(x - 2)

Depth = h

=> (x + 1)(x - 2)h = x³ + x²-4x-4

=> (x + 1)(x - 2)h = x²(x + 1) -4(x + 1) => (x + 1)(x - 2)h = (x² - 4)(x + 1)

=> (x - 2)h = (x² - 4) => (x - 2)h = (x + 2)(x - 2)

=> h = x + 2

x +2 to be Digged

V(x) = (x + 2)(x-2)(x + 1)

x=10 units, what is the volume of the sump

=> V(10) = (10 + 2)(10-2)(10 + 1) = 12 x 8 x

11 = 1,056 cubic units

x=4 units, what is the volume of the sump => V(4) = (4 + 2)(4-2)(4+1) = 6 x 2 x 5=

60 cubic units