Astronauts for NASA must measure between 62 and 75 inches tall. Which equation best represents the minimum and maximum heights accepted for NASA astronauts?
A. lh - 62] = 75
B. 1h - 131 = 6.5
C. |h - 6,5| = 68,5
D. \h - 68.51 = 6.5

Given:

Astronauts for NASA must measure between 62 and 75 inches tall.

To find:

The equation which best represents  the minimum and maximum heights accepted for NASA astronauts.

Solution:

Let h be the height accepted for NASA astronauts.

Astronauts for NASA must measure between 62 and 75 inches tall.

Subtract both sides by midpoint of 62 and 75, i.e., 68.5.

We know that, .

So, the absolute inequality for heights accepted for NASA astronauts is .

The equation of this inequality represents  the minimum and maximum heights accepted for NASA astronauts.

Using this equation we get , which are minimum and maximum values respectively.

Therefore, the correct option is D.

plz yuo

step-by-step explanation:

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.