Howard is standing 109 yards from the bottom of a water reservoir. he estimates that the angle of elevation to the top of the water reservoir is about 50°. about how far is howard from the top of the water reservoir?

70.1 yards

Step-by-step explanation:

See the attached diagram.

Let AC is the reservoir with A as the bottom and C is the top.

Now, B is the position of Howard which is 109 yards from A i.e. AB = 109 yards.

Again, the angle elevation from B to C is 50 degrees.

So, ∠ ABC = 50°  

Now,

⇒ x = 109 cos 50 = 70.1 yards.

Therefore, the distance between the top of the reservoir and Howard i.e. BC is equal to 70.1 yards. (Answer)

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)

35%

step-by-step explanation: