1. michelle purchased 25 audio files in january. in february she
purchased 40 audio files. find the percent increase. (lesson 5.1)

Michelle purchased 25 audio files in January. The percent increase is 60%

Solution:

Given Data:

Michelle purchases = 25 audio files in January

Again purchased = 40 audio files in February

We need to find the percent increase for the given data.

Step 1:

Use the formula for percent change ,

Step 2:

First we find the amount of change from the question.

Amount of change = 40 – 25  

By subtracting, we get 15.

Step 3:

substitute the values in formula we get,

Formula percent change = = 0.6  

Percent = 0.6 100 = 60 %.

Result:

Michelle purchased 25 audio files in January. And In February she purchased 40 audio files. Hence the percent increase is 60%.

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.