Line passing through (4,-1) and (3,-2)

y = x - 5

Solution:

Find the slope in order to find the line of equation

m= y2-y1/x2-x1

Take both the coordinates and name it A (4,-1) B(3,-2) for convenience  

m = -2 - (-1) / 3-4

m = -2 + 1 / -1

m = -1 / - 1 >>> m= 1

Now find the y intercept using the equation below

y=mx+ b

where  

y = y coordinate

m= slope

x= x coordinate  

b= y intercept  

SO  

Note: use any of the coordinate the answer would be the same in either case

I will be using the coordinate (4,-1)

y=mx+b

-1 = (4)(1) + b

-1 - 4 = b

-5 = b

y = x - 5

step-by-step explanation:

try remembering the steps

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.