Awhale descends 382.5 feet in 45 seconds. write an expression that can be used to find the average elevation change of the whale during its descent in, in feet per second.

The expression that can be used to find the average elevation change of the whale during its descent in, in feet per second is s =  8.5t

The formula for average elevation in feet per second is the speed of the whale in feet per seconds

Given the following parameters

Distance = 382.5 feet

Times = 45 seconds'

Calculate the speed

Speed = Distance/Times

Speed = 382.5/45

Speed = 8.5ft/s

Recall that s = d/t

d = st

s = 8.5t

Hence the expression that can be used to find the average elevation change of the whale during its descent in, in feet per second is s =  8.5t

Learn more here: link

Part a) The expression is  

Part b) -51 feet

Step-by-step explanation:

The complete question is

A whale descends 382.5 feet in 45 seconds.  

The whale's elevation changes at a constant rate.

Part a) Write an expression that can be used to find the average elevation change of the whale during its descent in feet per second

Part b) What is the elevation change of the whale after 6 seconds?

Part a)

we know that

Find out the unit rate

To find out the unit rate divide the total elevation by the total time

Remember that

The sea level represent the level zero

If a whale descends, then the elevation is negative (below the sea level)

so

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form

or

Let

x ----> the time in seconds

y ----> the elevation in feet

In this problem we have a proportional relationship, because the line passes through the origin (For x=0, y=0)

so

The value of the constant of proportionality k is equal to the unit rate or slope of the linear equation

substitute

Part b) For x=6 sec

substitute in the linear equation

any options?

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.