A machine part consist of a half sphere and a cylinder, as shown in the figure. the total volume of the part is blank pi c

Volume of the machine part = 114π inches³

Step-by-step explanation:

Volume of the machine part = Volume of cylinder + Volume of hemisphere

Volume of cylinder =

Where r = radius of the cylinder

h = height of the cylinder

Volume of the cylinder =

                                      = 108π inches³

Volume of the hemisphere =

                                             =

                                             = 6π inches³

Total area of the machine part = 108π + 6π

                                                   = 114π inches³

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)