Arectangle has side length of 8 inches and √3. which statement is true about the area of the rectangle?

a. it is a rational number because the product of the sides is the rational number 24.
b. it is an irrational number because the product of the two sides is 8 √3, an irrational number.
c. it is a rational number because the product of √3 and √3 results in 3, a rational number.
d. it is an irrational number because the product of the side lengths is √24, -! 84, an irrational number.

The correct answer is b. it is an irrational number because the product of the two sides is 8 √3, an irrational number.

Step-by-step explanation:

This is true because to find the area we multiply the length by the width. Since 8√3 cannot be expressed as a/b in which both a and b are both integers, then it is an irrational number.

Choice b is true.

Step-by-step explanation:

We have given the length and width of the rectangle.

length  = 8 inches And width = √3

We have to choose the true statement about area.

Area = length × width

Area  = 8 × √3

Area = 8√3

Since, we know that √3 is irrational number Hence, 8√3 is a irrational number.

Hence, Choice b is true.

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.

step-by-step explanation:

consider an orange peel: if you want to try and lay it flat, you have to stretch it, we know exactly how things are being stretched or squashed at any given point. we have many different map projections because each has different patterns of some projections can even preserve certain features of the earth without