While visiting a memorial, a person approximated the angle of elevation to the top of the memorial to be 35º. After walking 255
ft closer, he guessed that the angle of elevation had increased by 17º. Approximate the height of the memorial, to the top of the memorial.
1 answer:
Draw a diagram to illustrate the problem as shown in the figure below.
Let h the height of the hill. =
At position A, the angle of elevation is 40°, and the horizontal distance to the foot of the hill is x.
By definition,
tan(40°) = h/x h = x tan40 = 0.8391x
(1)
At position B, Joe is (x - 450) ft from the foot of the hill. His angle of elevation is
40 + 18 = 58°.
By definition, tan(58°) = h/(x - 450)
h = (x - 450) tan(58°) = 1.6003(x-450)
h = 1.6003x - 720.135 (2)
Equate (1) and (2).
1.6003x - 720.135 = 0.8391x 0.7612x = 720.135
x = 946.0523
From (1), obtain
h = 0.8391*946.0523 = 793.8 ft
Answer: The height of the hill is approximately 794 ft (nearest integer)
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Part A
<h3>Answer: T(n) = 58n+1800</h3>-------------
Work Shown:
1800 = initial cost or starting cost
58*1 = 58 = cost for one person
58*2 = 116 = cost for two people
58*n = cost for n people
58n+1800 = total cost
58n+1800 = T(n)
T(n) = 58n+1800
======================================
Part B
<h3>Answer: D(T) = 0.85T</h3>-------------
Work Shown:
T = total bill
15% discount means you still pay 85% of the bill (85%+15% = 100%)
D = discounted cost
D = 85% of T
D = 0.85*T
======================================
Part C
<h3>Answer: D(T(n)) = 49.3n + 1530</h3><h3>See attached image below for the table.</h3>-------------
Work Shown:
We combine parts A and B.
T(n) = 58n+1800 from part A
D(T) = 0.85*T from part B
D(T(n)) = 0.85*( T(n) )
D(T(n)) = 0.85*( 58n+1800 ) ... plug in T(n) = 58n+1800
D(T(n)) = 0.85*( 58n+1800 )
D(T(n)) = 0.85*(58n)+0.85*(1800) ... distribute
D(T(n)) = 49.3n + 1530
If we plugged in n = 0, then,
D(T(n)) = 49.3n + 1530
D(T(0)) = 49.3*0 + 1530
D(T(0)) = 1530
Or we could plug n = 0 into T(n) to get T(0) = 1800
Then plug T = 1800 into D(T) = 0.85*T to get D(1800) = 1530
Either way you'll get the same answer.
Repeat this (using either method) for n = 50, 100, 150, 200 and you'll get the table of values you see below in the attached image.
======================================
Part D
The D( T(n) ) function allows us to find the discounted cost D for any number n of people that show up.
The input is n, where n is some positive integer less than or equal to 200 (because this is the reception hall's max capacity).
The output is the final discounted cost.
Example: n = 50 is one input which leads to its corresponding output of D( T(n) ) = 3995 as the table shows. So 50 people would have a discounted total cost of $3,995.
