Two planes left the same airport traveling in opposite directions. the first plane left at 9: 00 a. m. and 2.25 hours later, the two planes were 1825 miles apart. the second plane left at 10: 00 a. m. and its average rate was 108 miles per hour slower than the first plane's average rate. let x represent the first plane's average rate. what was the first plane's average rate?

x = 560 miles/hr

Step-by-step explanation:

Let speed of first plane = x

Let speed of second plane = y

x-y =108 (first plane is faster)

It took first plane 2.25 hrs to be 1825 miles apart.

Distance moved after 2.25 hrs =2.25x

It took second plane 1.25 hrs to be 1825 miles apart

Distance moved after 1.25 hrs =1.25y

So 2.25x + 1.25y = 1825 1

Put x = 108+y in eqn 1

2.25(108+y) + 1.25y= 1825

243 + 3.5y = 1825

3.5y= 1582

y = 452

x = 108 + 452 = 560 miles/hr

42.4

step-by-step explanation:

convert to decimal

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.