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 three 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?

enter your answers in the boxes.

ft by

material=wall+2*side and material is 40 ft

so: 40 = w + 2sw = 40 - 2s

Area = ws, using w from above we get:

A=(40-2s)s

A=40s-2s^2d

A/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

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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