The table shows values for functions f(x) and g(x) .
x f(x) g(x)
−2 −8 −2
−1 −1 −1
0 0 0
1 1 1
2 8 2
what are the known solutions to f(x)=g(x) ?
select each correct answer.
−2
−1
0
1
2

-1, 0 and 1

Step-by-step explanation:

Let's work through this step by step.

x goes from -2 to 2 so we will check each integer in between.

f(-2) and g(-2) is the first one.  The table shows f(-2)=-8 and g(-2)=-2, so f(-2) does not equal g(-2)

Now we just keep doing this for x=-1,0,1, and 2

f(-1) = -1 and g(-1) = -1 so f(-1)=g(-1)

f(0)=0 and g(0)=0 so f(0)=g(0)

f(1)=1 and g(1)=1 so f(1)=g(1)

f(2)=8 and g(2)=2 so f(2) does not equal g(2)

So there were three xs that made f(x) = g(x).  -1, 0 and 1, so those are your answers.  

16.9 times 2.85

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.