Sprinkler heads come in all different sizes depending on the angle of rotation desired. If a sprinkler head rotates 90 ° and has enough pressure to keep a constant 25-foot spray, what is the area of the sector of the lawn that gets watered? Round to the nearest square foot.

491 ft²

Step-by-step explanation:

We know the area of a sector, A = Ф/360° × πr² where Ф = angle subtended by sector = angle of rotation of sprinkler = 90° and r = radius of sector = length of spray = 25 feet.

Substituting the values of the variables into the equation, we have

A = Ф/360° × πr²

A = 90°/360° × π(25 ft)²

A = 1/4 × 625π ft²

A = 1/4 × 1963.5 ft²

A = 490.9 ft²

A ≅ 491 ft² to the nearest square foot

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)