Posted by Anonymous on Wednesday, April 4, 2012 at 2:09pm.
A simple rain gutter is constructed using a sheet of aluminum that is 40cm wide. The edges are turned up to form right angles. Determine the depth of the gutter that will maximize the cross-sectional area (allowing the greatest amount of water to flow).
I don't know where and how to start.
please help and thank you
- math problem - Reiny, Wednesday, April 4, 2012 at 2:28pm
make a sketch.
Assuming that the gutter is rectangular and the sides must have the same height, look at the cross section of the gutter.
let the base by y and each of the sides by x
we know that
2x + y = 40
y = 40-2x
the area A of the cross-section will be
A = xy
= x(40-2x) = 40x - 2x^2
Assuming this is a typical Calculus question ...
dA/dx = 40 - 4x = 0 for a max of A
40-4x = 0
x = 10
the the depth will be 10 cm
if you don't know Calculus , you will have to complete the square on
A = 40x - 2x^2
- math problem - Anonymous, Wednesday, April 4, 2012 at 2:43pm
I don't know calculus
This is what I got after completing the square:
How do I know what is the depth when I complete the square?
Answer this Question
More Related Questions
- pre-calc - construction of a rain gutter: a piece of rectangular sheet metal is ...
- Pre-Calc) - a piece of rectangular sheet metal is 20 in wide. It's to be made ...
- geometry - a piece of rectangular sheet metal is 20 in. wide. It is made into a ...
- calculus - A long rectangular sheet of metal, 12 inches wide, is to be made into...
- mathematics - Please help me answer this question; 1.A metal gutter open at the ...
- math - You are designing a rain gutter made from a piece of sheet metal that is...
- Geometry - 1. An airplane is flying at 36,000 feet directly above Lincoln, ...
- MATH - a ball of radius 1 is dropped into a V-shaped gutter. The ball touches ...
- math - a ball of radius 1 is dropped into a V-shaped gutter. The ball touches ...
- math - A gutter cleaner wants to reach a gutter 40 ft above the ground. Find the...