Given:
Height of Mountain A = 5210 feet
Distance of Mountain A from a helicopter above the peak = 1000 feet
Angle of depression:
Mountain B to helicopter = 43 degrees
Mountain B to Mountain A = 19 degrees
First, draw an illustration and label the enumerated given values.
Observe that there are two right triangles formed:
From the triangle formed by the helicopter and Mountain B,
let x = total height of mountain B
y = leg of first triangle (helicopter and mountain b)
h = hypotenuse
Use the Pythagorean Theorem:
cos (43) = y / h
From the second triangle formed by mountain b and a,
cos (19) = (1000 + y) / h
solve for h and y
then, solve for the height of Mountain B:
x = 1000 + y + 5210
Answer:
Smallest rate for the train is 50 mph and largest is 60 mph.
For the bus it is 25 and 30 mph.
Step-by-step explanation:
If the speed of the train is 2x then speed of the bus is x mph, and the train travels twice as far as the bus in a given time.
Distance = speed * time
For the largest rate:
d = 2x * 0.5 for the train
x = d
0.5d = x for the bus
d - 0.5d = 15
0.5d = 15
d = 30
So the rate for the train = 30 / 0.5 = 60 mph.
In a similar fashion we can show that the smallest rate for the train is
25/ 0.5 = 50 mph.
Answer: 76 Sodas and 40 hot dogs
Step-by-step explanation:
Let S and H represent the numbers of Sodas and Hot dogs.
We are told that:
S + H = 116
We also see that:
H = S - 36
==
Take the second equation's value for H (S - 36) and use it in the first:
S + H = 116
S + (S-36) = 116
2S = 152
S = 76
and therefore H = S - 36, or 40.
76 + 40 = 116 [Checks]
76 Sodas and 40 hot dogs
B) 4.90
Hope that helped :)
