7x²-26x-8=0
solving polynomial equations with factoring, algebra. me!

Step-by-step explanation:

7x² - 26x - 8 = 0            

Find two numbers whose product equals (7)(-8) and sum equals -26.

                        -28 × 2 = 56, -28 + 2 = -26

Replace -26x with -28x + 2x:      7x² - 28x + 2x - 8 = 0

Factor the left two terms & right two terms:    7x(x - 4) + 2(x - 4) = 0

Notice that both sides have a common factor of (x - 4)  -->  This is one of the factors.  The other factor is what is on the outside of (x - 4) --> 7x + 2

Rewrite the expression as two factors:   (x - 4)(7x + 2) = 0

set each factor equal to zero and solve for x.

              x - 4 = 0                7x + 2 = 0

                   x = 4                 7x       = -2

                                              x      

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.