:the imbrium basin is the largest basin on the moon. a reasonable domain
for the height above the lowest point in the basin is given by
{d0 < d < 3805774}. what does this tell you about the basin?

Part a)

It takes 1.57 seconds for an object to fall a distance of 2 feet

Part b) see the explanation

Part c)

Step-by-step explanation:

The complete question is

On the moon, the time, in seconds, it takes for an object to fall a distance, d, in feet, is given by the function f(d) = 1.11√d.

Part a: determine f(2) and explain what it represents.

Part b: The imbrium basin is the largest basin on the moon. A reasonable domain for the height above the lowest point in the basin is given by {d|0 ≤ d ≤ 3805774}. What does this tell you about the basin.

Part c: how long would it take a rock to drop from the rim to the bottom of the basin?

Let

f(d) -----> the time in seconds it takes for an object to fall

d -----> distance in feet

we have

Part a): Determine f(2) and explain what it represents

we know that

f(2) represent the time in seconds it takes for an object to fall a distance of 2 feet

For d=2 ft

substitute in the function above and solve for f(2)

therefore

It takes 1.57 seconds for an object to fall a distance of 2 feet

Part b) The imbrium basin is the largest basin on the moon. A reasonable domain for the height above the lowest point in the basin is given by {d|0 ≤ d ≤ 3805774}

What does this tell you about the basin?

The height of the basin is greater than or equal to 0 ft and less than or equal to 3,805,774 ft  

so

The maximum height of the basin is 3,805,774 ft

Part c) How long would it take a rock to drop from the rim to the bottom of the basin?

we know that

The distance from the rim to the bottom of the basin is equal to the maximum height of the basin

so

substitute the value of d in the function f(d)

x = -2

y = 848

step-by-step explanation:

plug in the numbers

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.