a plane flies a straight course. On the ground directly below the flight path. observers 2 miles apart spot the plane at the sam
e time. The planes angle of elevation in 46 degrees from on observation point and 71 degrees from the other. How high is the plane?
1 answer:
Kindly refer to the attached figure for reference
Let A and B be the two points where we have the two observers. Let C be the point above at which the plane flies
Angle A = 46 degrees and Angle B = 71 degrees
AB = 2 miles
Let AD = x , then DB = 2-x
Let the vertical distance between the plance and ground represented by CD be y
As per trigonometric functions, tan θ = opposite side/adjacent side
tan 46 = y/x
tan 71 = y/(2-x)
tan 46 = 1.03553
tan 71 = 2.90421
1.03553 = y/x
y = 1.03553x
2.90421 = y/(2-x)
2.90421*(2-x) = y
5.80842 - 2.90421x = y
5.80842 - 2.90421x = 1.03553x
5.80842 = 3.93974x
x = 1.4743 miles
y=1.03553x
y = 1.4743 * 1.03553
y =1.5267 miles
CD = 1.5267 miles
The plane is 1.5267 miles from the ground
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Answer: 4
Step-by-step explanation:
Let N be the total number of runs.
The microscopes per year will be equal to the total number of runs * microscopes per run
total number of microscopes = total number of runs * microscopes per run
now we have each run to cost 2500, therefore:
run costs = 2500 * total runs = 2500*N
we also have insurance and storage costs (note the average thats why we divide by 2):
storage costs = 20* microscopes per run /2 = 20*N/2
insurance costs = 15 * microscopes per run = 15*N
the costs are:
costs = run costs + storage + insurance
now the comany sells 1600 microscopes a year, so in order to figure out the number of microscopes per run we divide 1600 by the total number of runs N and replace in the costs
costs = 2500N + 40000/N => C(N) = 2500N + 40000/N
now derivate the function with respect to N and equal to 0:
this gives you two solutions, N = -4 which is not eligible (you cant make negative microscopes lol) and N = 4 which is the answer
have a nice day