Joe is climbing the ladder and stops when his feet are vertically 3.2 feet above the ground and horizontally 2.4 feet from the base of the ladder.

which equation represents this new situation and can be used to find how far joe climbed up the ladder?

select the correct answer.

1.3.22 + b2 = 2.42
2.3.2 + 2.4 = c
3.3.22 + 2.42 = c2
4.a2 + 2.42 = 3.22

The correct answer is the third option that is

Step-by-step explanation:

An image is attached with it.

Lets say that is the wall and measuring feet is the ladder length.

Now as Joe is climbing on it.

It moves horizontally taking it as direction from the base then it also climb upward considering it as .

We see that the situation where we have drawn the ladder and the support (wall) it forms a right angled triangle.

So for this, the ladder is equivalent to the hypotenuse of the triangle.

And from Pythagoras formula for a right angled triangle we know that:

Here the base and perpendicular .

So the hypotenuse/ladder which is .

The situation which can be used to find how far Joe has climbed up the ladder =

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.

i agree because i see the other persons thinking is clear