Write an English phrase that would translate into the following mathematical expression. 8(2-6)
Which of the following is equivalent to the expression 8(z - 6)??

B. 8 times the difference of a number z and 6

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Translate (z - 6)

z = a number z

- = difference

6 = six

(z - 6) = The difference between a number z and 6

Step 2: Translate 8(z - 6)

(z - 6) = The difference between a number z and 6

Since we are distributing the 8, we are multiplying.

8 times the difference of a number z and 6

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.

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0