Answer:
The farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.
Step-by-step explanation:
The question tests the applications of differential calculus. We are informed that the farmer will use the wall of his barn as one side of the enclosure implying that the 144 feet of fencing will only be used to form the three remaining sides of the rectangular enclosure.
If we let x denote the width of this rectangular enclosure to be formed, then its length will be 144-2x since we shall be having two sides each measuring x and the total length of the fencing is 144. 2x will be used on the width leaving 144-2x for the length since one side of the length is formed by the wall.
If we let A denote the area of the rectangular enclosure, then;
A = x(144 - 2x)
since the area of a rectangle is simply the product of the length and the width. We open the brackets;
A = 144x - 2x^2
Clearly, the Area is a function of the width that is A is the dependent variable while x is the independent one.
At the maximum area, the slope of the tangent to the curve 144x - 2x^2 is 0. Therefore, we differentiate the given function of x with respect to x then set the resulting expression to 0 to determine x that will maximize A;
dA/dx = 144 - 4x
We set this expression to 0 and solve for x;
144 - 4x = 0
144 = 4x
x = 36
Therefore, the farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.
9514 1404 393
Answer:
the graph increases
Step-by-step explanation:
If you read your problem statement, you find it tells you the answer:
"... point A and then continues to increase through B"
That is, between points A and B, ...
the graph increases
Answer:
$51
Step-by-step explanation:
do 13*3 because of the 2 kids and the adult then add 12 because of the snacks
hope this helps
Answer:
44% cahnce
Step-by-step explanation:
To solve this, add up all the customers. Then, divide the amount of debit card customers, by the total amount of customers. This will give you percentage of people who paid in debit, which is also the probability:
20+26+13
=
59
This is the amount of customers. Now we divide:
26/59
=
0.4406
Remember that to create percentage, you must multiply the decimal by 100:
0.4406*100
=
44.06%
The .06 is so small that it doesnt need to be kept in this percentage:
44%
So this is you answer!
Hope it helps! :)
