Running from the top of a flagpole to a hook in the ground there is a rope that is 58 feet long. If the hook is 40 feet from the base of the flagpole, how y'all is the flagpole?

Therefore,

42 feet tall is the flag pole.

Step-by-step explanation:

Given:

Let the top of the flag pole be denoted as A, Base of flag pole as B, and the hook on the ground as C as shown in the figure,

Such that,

Length of rope from the top of flag pole = AC = 58 feet

Length between flag pole base and the hook = BC = 40 feet

To Find:

Length of flag pole = AB = ?

Solution:

In Right Angle Triangle ABC, By Pythagoras theorem

Substituting the values we get

Therefore,

42 feet tall is the flag pole.

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.