Find the exact value of 75(degrees); leave answer in simplest radical form. Enter terms under the radical in number order.

sin 75 = sin(45 + 30) =

sin75º=sin(30)º+45º)

=sin 30 cos 45+cos 30 sin 45

=1/2*√2/2+√3/2*√2/2

=√2/4+√6/4

=(√2+√6)/4

Check with calculator:

sin 75º≈0.9659

exact value=(√2+√6)/4≈0.9659

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)