If AB=2(x+1) BC=3x+1 and AC=4(x+2) then find the value for X. AB, BC and AC

Givens

AB + BC = AC

AB = 2(x + 1)

BC = 3x + 1

AC = 4(x + 2)

Substitute and Solve

AB + BC = AC

2(x + 1) + 3x + 1 = 4(x + 2)     Remove the brackets on the left

2x + 2 + 3x + 1 = 4(x + 2)      Collect the like terms on the left

5x + 3  = 4(x + 2)                  Remove the brackets on the right.

5x + 3 = 4x + 8                     Subtract 4x from both sides.

5x - 4x + 3 = 8            

x + 3 = 8                               Subtract 3 from both sides

x =8 - 3

x = 5

Answers

AB=2(5 + 1) = 2 * 6 = 12

BC = 3x + 1 = 3*5 + 1 = 15 + 1 = 16

AC = 4(5 + 2) = 4*7 = 28

Step-by-step explanation:

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.

you already gave the answer

step-by-step explanation: