SOLUTION: The city wants to dig a tunnel under the New York canal to create another underground road to clear up the heavy traffic the city has been experiencing lately. The blueprints show

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Question 1195588: The city wants to dig a tunnel under the New York canal to create another underground road to clear up the heavy traffic the city has been experiencing lately. The blueprints show that the tunnels path is demonstrated by the quadratic relation h = 0.25d2 - 2.5d + 2.75. All of these (d represents horizontal distance in kilometers, h represents height in meters).
a. What is the height at which the city began to dig?
b. What is the total horizontal distance of the underground part of the tunnel ?
c. What is the minimum point at which the city digs below the ground?
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The city wants to dig a tunnel under the New York canal to create another underground road to clear up the heavy traffic the city has been experiencing lately.
The blueprints show that the tunnels path is demonstrated by the quadratic relation h = 0.25d^2 - 2.5d + 2.75.
All of these (d represents horizontal distance in kilometers, h represents height in meters).
Here is the graph
+graph%28+300%2C+200%2C+-6%2C+12%2C+-6%2C+10%2C+.25x%5E2-2.5x%2B2.75%2C+2.75%2C+-3.5%29+
a. What is the height at which the city began to dig?
That would be when d=0, therefore 2.75 meters
:
b. What is the total horizontal distance of the underground part of the tunnel ?
Assume it's considered underground when d is less than 2.75 then the horizontal distance would be 10 km
If you assume it is underground when d is negative, then solve for 0 with the quadratic formula and you get d=1.25 and 8.74.
8.74 - 1.25 ~ 7.5 km is the horizontal distance underground
;
c. What is the minimum point at which the city digs below the ground?
find the axis of symmetry using x=-b/(2a)
d = %28-%28-2.5%29%29%2F%282%2A.25%29
d = 5 km when min height occurs
find the lowest value
.25*5^2 - 2.5*5 + 2.75 = 3.5 meters

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I did a similar solution to this one, then noticed that the units don't match.
d is in kms, h is in meters.
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I'll redo it tomorrow and post it.