Find the minimum length of fence needed for a play area with area 60.5 m2. What are the dimensions of the play area?

The answer is below

Step-by-step explanation:

Let x and y represent the length and the width of the play area. Hence:

xy = 60.5

y = 60.5 / x

The perimeter (P) of the play area is given as:

P = 2(x + y)

substitute for y:

P = 2(x + 60.5/x)

P = 2x + 121/x

The minimum area is at P' = 0. Hence:

P' = 2 - 121/x²

0 = 2 - 121 / x²

121 / x² = 2

x² = 60.5

x = √60.5

Also, y = 60.5 / x = 60.5 / √60.5

y = √60.5

Therefore the minimum perimeter is:

P = 2(√60.5 + √60.5) = 31.11 m

whatever you can spend with $11.53 or under.

step-by-step explanation:

20 - 8.47 = 11.53. take away the money he used for lunch from the starting amount of 20.

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.