Hey guys I need can someone me help get started on these two word problems.
An archway over a road is modeled by the quadratic function y < -.1x^2+12.
Can a car 6 feet wide and 7 feet high fit under the arch without crossing the median line?
You have 80 feet of fence to enclose a rectangular garden, The function a = 40x-x^2 gives you the area of the garden in sqft where x is the width. What width gives you the maximum gardening area? what is the maximum area?
Ok, if it can't cross the median, then the road must be 12 feet wide at a height of 7 feet or more. Or put another way, 6 feet from the centerline (y axis), the curve must be at a height of y > 7 feet. This is easy by simply graphing it, but not much harder to work out without graphing it.
So, how high is the curve at x = 6?
Let me see if I can help you with the second one:
We have area= and we can also deduce as we have 80 feet of fence, so . Now we need to turn this into one equation so:
Now solve the two together:
Now find the vertex, I used which gives 20.5. Now substitute 20.5 into the quadratic and solve for y.
I get the maximum area to be 380.25 feet^2.
I hope this helps and that I got it correct - I am sure someone will correct me if I am wrong!