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.
Answer:x=−24/11
Step-by-step explanation:
Simplifies to:
x−86x=79
Let's solve your equation step-by-step.
x−86x=79
Step 1: Cross-multiply.
x−86x=79
(x−8)*(9)=7*6x
9x−72=42x
Step 2: Subtract 42x from both sides.
9x−72−42x=42x−42x
−33x−72=0
Step 3: Add 72 to both sides.
−33x−72+72=0+72
−33x=72
Step 4: Divide both sides by -33.
−33x−33=72−33
x=−2411
the answer is D) because the line is curved
Answer:
5 : 1
Step-by-step explanation:
From your second-grade memorization of multiplication tables, you recognize that 15 = 3×5, so you know 3 is a factor of both numbers in the ratio. To reduce the ratio to simplest form, you divide out all common factors:
15 : 3 = (15/3) : (3/3) = 5 : 1
Answer:
26
Step-by-step explanation:
h represents highschool members
m represents middle school members
42 = h+m
h = 2m-6
Substitute h for 2m-6 in first equation:
42 = (2m-6)+m
Solve for m:
42 =3m-6
48 = 3m
m = 16
Subsitute 16 for m in second equation:
h = 2(16)-6
Solve for h:
h = 32-6
h = 26
