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?
Thanks.
Did you mean y = and not y < perhaps? Hard to say for sure otherwise.
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?
Hi Jubbly
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!