A rain gutter is made from sheets of aluminum that are 22 inches wide by turning up the edges to form right angles. Determine th
e depth of the gutter that will maximize its cross- sectional area and allow the greatest amount of water to flow. What is the maximum cross-sectional area?
1 answer:
So hmm notice the picture below
thus, the perimeter of the gutter is just w + w + l, or 2w +l
thus
take the derivative of A(w), zero it out, check any critical points in the interval of (0, 22), for a maxima
recall, the aluminum sheet is just 22inches long, thus, whatever the "depth" or "w" is, has to be more than 0, and less than 22
thus, the perimeter of the gutter is just w + w + l, or 2w +l
thus
take the derivative of A(w), zero it out, check any critical points in the interval of (0, 22), for a maxima
recall, the aluminum sheet is just 22inches long, thus, whatever the "depth" or "w" is, has to be more than 0, and less than 22
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Hey there! The answer is 7x + 4y < 40
Let's first rearrange our data in a more structured way.
x represents a box of wings which has a cost of $7.00. Therefore the total cost of the boxes is 7x.
y represents a tray of nachos which has a cost of $4.00. Therefore the total cost of the trays is 4y.
The sum of the costs of trays and boxes, which is (7x + 4y) must be smaller than $40.
Now we can set up the inequality.
~ Hope this helps you!
Let's first rearrange our data in a more structured way.
x represents a box of wings which has a cost of $7.00. Therefore the total cost of the boxes is 7x.
y represents a tray of nachos which has a cost of $4.00. Therefore the total cost of the trays is 4y.
The sum of the costs of trays and boxes, which is (7x + 4y) must be smaller than $40.
Now we can set up the inequality.
~ Hope this helps you!