Adiver is exploring the waters of the great barrier reef.

part a. she is currently -5 feet from the surface of the water and plans to explore a shipwreck that is at -75 feet from the surface. if she moves at a rate of -8 feet per minute, how many minutes does it take the diver to reach the shipwreck?

part b. when she is done exploring the reef, she ascends at a rate of 5 feet per minute. once she reaches a height of -30 feet, she must rest for 15 minutes to allow her body to adapt to the changing water pressure. she then continues to the surface at the same rate. how long does it take the diver to reach the surface?

Step-by-step explanation:

Part A

The change in depth from -5 ft to -75 ft is ...

  -75 -(-5) = -70 ft

At the rate of -8 ft/min, it will take this long to reach the desired depth:

  time = distance/speed

  = (-70 ft)/(-8 ft/min) = 70/8 min = 8 3/4 min

__

Part B

Ascending from -75 ft to 0 ft at the rate of 5 ft/min will take ...

  time = distance/speed

  = (0 -(-75 ft))/(5 ft/min) = 75/5 min = 15 min

Adding a 15 minute rest will bring the total travel time to ...

  (15 min) + (15 min) = 30 min

34

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.