Joe will build a rectangular pen for his dog. A wall will form one side of the pen. Joe has 40 ft of fencing to form the other t

Question

3 years ago

12

Joe will build a rectangular pen for his dog. A wall will form one side of the pen. Joe has 40 ft of fencing to form the other t

hree sides.
Joe plans to build the pen so that it has its maximum possible area.

What will be the dimensions of Joe’s dog pen?

Mathematics

2 answers:

Svetlanka [38] · Answer 1 · 2022-02-09T23:26:13+03:00

Material=wall+2*side and material is 40 ft so:

40=w+2s

w=40-2s

Area=ws, using w from above we get:

A=(40-2s)s

A=40s-2s^2

dA/ds=40-4s and d2A/ds2=-4

Since d2A/ds2 is a constant negative acceleration, when dA/ds=0, A(s) is at an absolute maximum.

dA/ds=0 when 4s=40, s=10 ft

And since w=40-2s, w=20 ft

So the dimensions of the pen are 20 ft by 10 ft, with the 20 ft side being opposite the wall. And the maximum possible area is thus 200 ft^2

Alja [10] · Answer 2 · 2022-02-10T01:39:51+03:00

Answer:

The <em>dimensions</em> are 20 ft by 10 ft.

Step-by-step explanation:

I just took this quiz and put the answer 200 by 200 ft. And I got it wrong because they asked for the dimensions. The other person's answer is correct, but in the wrong form! Thanks for the help and support on brainly!!!