How will the solution of the system y>2x+2/3 and y<2x1/3 change if the inequality sign on both inequalities is reversed

We have the inequalities:

y > 2*x + 2/3

y < 2*x + 1/3

First, we need to understand how to see the solutions of each one of these.

y > 2*x + 2/3

The solution set of this inequality will be ALL the points above the line:

y = 2*x + 2/3

And the solution of the inequality:

y < 2*x + 1/3

Will be the set of all the points below the line:

y = 2*x + 1/3

Notice that line "y = 2*x + 2/3" is above than the line "y = 2*x + 1/3"

Then the system:

y > 2*x + 2/3

y < 2*x + 1/3

Has no solutions.

If we reverse both inequalities, we will get:

y < 2*x + 2/3

y > 2*x + 1/3

Now the solution of the first inequality will be all of the region below the line, and the solution for the second will be all the region above the line.

In this case, the solution of the system will be all the region between both lines, as we can see on the graph below. Where the solution of the system is the doubled shaded area.

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.

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )