19. Find the base circumference of a cone with
height 5 cm and volume 125cm3.

circumference = 30.6998 cm

Step-by-step explanation:

Use the formula

Volume = (1/3) * π * r^2 * h

We have:

125 cubic cm =  (1/3) *π * r^2 * 5 cm

solve for the radius r

3 * 125 / (5* π)   =  r^2

r^2 =   75/π

r =  square root ( 75/π ) cm  = 4.886 cm

circumference =   2*π*r  =  2*π *  ( ) =   2 * 5 * root(3 * pi)=  30.6998 cm

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

thats not a system of equations, that is a solution