Laura has let out 60 m of her kite string, which makes an angle of 68º with the ground. What is the height of the kite?

Step-by-step explanation:

The set up will form a right angled triangle. The distance that Laura let out her kite string will be the hypotenuse of the triangle, the angle that the kite makes with the ground will be the angle of elevation, facing the height of the kite.

The height of the kite H, will be the opposite side of the triangle since it is facing the angle directly.  based on the trig identity SOH;

sintheta = opposite/hyp

sin68° = H/60

H = 60sin68°

H = 55.6m

The height of the kite is 55.6m

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)

i think it’s a i believe