a concrete block has a volume of 756 cubic meters and the dimensions are (3x-4),(2x-3) and x find the value of x

Answer 1

A concrete block has the shape of a rectangular prism. remember the volume (V) of a rectangular prism can be expressed as V = lwh, where l, w, and h, are the length, width, and height of the object respectively. In this case, you are given those values in the form of the dimensions (3x-4),(2x-3) and x.

So you can write out the equation as V = lwh = x(2x-3)(3x-4) = 756

To solve for x, you need to multiply out the expression, simply, and then solve the resulting cubic equation. Leaving this exercise to you. Happy to walk you through it if you schedule some time with me.

Remember that you need positive values of x as the solutions, as only those make sense in the context of your problem.

Answer 2

756 = x(3x-4)(2x-3)

x(6x^2-17x+12) = 756

6x^3 -17x^2 +12x -756 = 0

'by Descartes sign rule there are 1 or 3 positive real solutions, no negative real solutions, and 2 or 0 imaginary solutions

use the relatively unknown cubic formula

or graph the equation and find the x intercept(s) = 6 meters = x. if only one x intercept then the other two solutions are imaginary

x=6, 3x-4 = 14, 2x-3 = 9

6(14)(9) = 84(9)=756

dimensions are 6 by 14 by 9

Answer 3

See the videa.