Question

Atharv wants to bulld a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Atharv has 700 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let
w
be the width of the enclosure (perpendicular to the barn) and let
l
be the length of the enclosure (parallel to the barn). Write an function for the area
A
of the enclosure in terms of
w
. (HINT first write two equations with
w
and
l
and
A
. Solve for
l
in one equation and substitute for
l
in the other).
A(w)=
b) What width
w
would maximize the area?
w=
c) What is the maximum area?
A=
square feet Given the function
g(r)=(r−3)(r+6)(r−4)
its
g
-intercept is its
r
-intercepts are Given
P(x)=x 3
−3x 2
−8x+4
, use the Remainder Theorem to find the Remainder when
P(x)
is divided by
(x−2)
R=
Use the Factor Theorem to determine whether
(x−2)
is a factor of
P(x)
Type yes or no for your answer. Yes No

Answer 1

The function of the area of the rectangle is A = 700w - w^2

The perimeter of the rectangle = 2(l + w)

Where l is the length of the rectangle

w is the width of the rectangle

The total length of the fencing = 700 feet

The one side will be against barn, therefore there is no fencing

Then the perimeter will be

l + 2w = 700

l = 700 - 2w

The area of the rectangle = l × w

Where l is the length and w is the width of the rectangle

The area of the rectangle = (700 - 2w)w

= 700w - 2w^2

Therefore, the area is A = 700w - 2w^2

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