The underside of a bridge has a shape of a parabolic arch. It has a maximum height of 30m and a width of 50m. Can a sailboat with a mast of 28m above the water pass under the bridge 8m from the middle of the bridge?
no I did not know I had to show my work,I did not read the posting tips, I have posted most of my work to show where I was stuck. I did not expect to have my homework just done for me as that would be useless when it came time to write the test or final exam. I am just not grasping how to interpret the word problems correctly into the quadratic equations, that is the part I am stuck on, not the actual equation. Does this make sense?
Sorry Ms. Sue, I have posted hopefully correct or on the right track answers to all the other questions, but I have to go to sleep, I will attempt to answer this tomorrow Thanks
To determine if a sailboat with a mast of 28m can pass under the bridge, we need to compare the height of the mast with the height of the bridge at the given distance from the middle.
Since the bridge has a shape of a parabolic arch, we can assume it follows the equation of a parabola, which is in the form of y = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola.
In this case, the maximum height of the bridge is 30m, which is the vertex of the parabola. Therefore, the vertex form equation of the parabola is y = a(x-0)^2 + 30, which simplifies to y = ax^2 + 30.
To find the value of 'a' and determine the equation of the parabola, we can use the given width of the bridge.
At the widest point of the bridge (x = ±25m), the height is 30m, so we can substitute these values into the equation:
30 = a(25)^2 + 30
0 = a(625)
a = 0
Since the coefficient 'a' is zero, it means the equation of the parabola becomes y = 0x^2 + 30, which simplifies to y = 30.
From the equation of the parabola, we see that the height of the bridge is a constant 30m, irrespective of the distance from the middle.
Now, to determine if the sailboat can pass under the bridge, we need to check if the mast's height (28m above the water) is less than the height of the bridge.
At a distance of 8m from the middle, the height of the bridge is still 30m, which is greater than the mast height of 28m. Therefore, the sailboat can pass under the bridge 8m from the middle.
In conclusion, based on the given dimensions and calculations, the sailboat with a mast of 28m can pass under the bridge 8m from the middle.
Did you read this before you posted your umpteen math problems?
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