h=7/5d-d^2/100 where h is the height of the arch above the road in meters.
Not actually looking to have all completed, but give advice on how to achieve the results
a. where does the arch and road come together?
b.How far is it from where the arch begins on the left and where it ends on the right end of the bridge?
c.If you are one-fourth of the way along the bridge how high above you is the arch?
d.How far along the bridge do you need to walk from the left end to get to apoint where the arch is 20m above the road?
Is this the correct approach to start?
h=7/5d-d^2/100
clear fractios by multiplying all by 500
0=700d-5d^2
5d^2-700d=0
5d(d-140)=0
ok so far
so if 5d(d-140) = 0
d = 0 or d = 140
(visualize the bridge starting at d=0 and going to d=140
so it is 140 m wide at the base
c) if you are 1/4 way along the road, d = 35
h = (7/5)(35)) - 35^2/100 = 36.75
d) to have h = 20
(7/5)d - d^2/100 = 20
multiply by 100
140d - d^2 = 2000
d^2 - 140d + 2000 = 0
d = 123.85 or d = 16.148
Notice you would be 20 m below the bridge at both ends of the bridge.
Yes, your approach is correct so far. You correctly rearranged the equation and simplified it to the quadratic equation 5d^2 - 700d = 0. Now, to find the solutions to this equation, you can either factor it or use the quadratic formula.
To factor the equation, you can notice that both terms have a common factor of d, so you can factorize it as follows:
d(5d - 700) = 0
Now, set each factor equal to zero and solve for d:
d = 0 (which represents the left end of the bridge)
5d - 700 = 0
d = 140 (which represents the right end of the bridge)
So, according to this equation, the arch begins at the left end of the bridge (d = 0) and ends at the right end of the bridge (d = 140).
Now let's move on to answering the specific questions:
a. To determine where the arch and road come together (or the height of the arch above the road at that point), substitute d = 0 into the equation and solve for h.
b. To find the distance between the beginning of the arch on the left and the end of the arch on the right, subtract the two values of d.
c. To calculate the height of the arch when you are one-fourth of the way along the bridge, substitute d = (1/4) * total distance of the bridge into the equation and solve for h.
d. To determine how far along the bridge you need to walk from the left end to reach a point where the arch is 20m above the road, substitute h = 20 into the equation and solve for d.
Let me know if you need further assistance with any of these steps or any other questions you have!