Problema Solution
Building a 200 ft long bridge across Scorpion Gulch, where the water
is 8 feet deep, costs $700,000. Assume that the cost varies directly
with the length of the bridge and directly with the square of the
depth of the water. Write the particular equation expressing cost in
terms of length and depth. Use the equation to predict the cost of a
bridge downstream from the present one, where the water is only 5 feet
deep but the length must be 600 feet.
Answer provided by our tutors
Let
C = the cost of the bridge
L = the length of the bridge
D = the depth of the water
C = k*L*D^2, where k is constant
L = 200 ft
D = 8 ft
C = $700,000
700000 = k*200*8^2
........
........
k = 54.6875
The particular equation expressing cost in terms of length and depth is:
C = 54.6875*L*D^2
L = 5 ft
L = 600 ft
We plug the values into the equation C = 54.6875*L*D^2
C = 54.6875*600*5^2
........
........
C = $820,312.50
The cost of the bridge would be $820,312.50.