The question is incomplete. Here is the complete question.
Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -
x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answer: L = 1; W = 9/4; A = 2.25;
Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:
A = x.y
A = x(-
)
A = -
To maximize, we have to differentiate the equation:
= 
(-)
= -3x + 3
The critical point is:
= 0
-3x + 3 = 0
x = 1
Substituing:
y = -x + 3
y = -.1 + 3
y = 9/4
So, the measurements are x = L = 1 and y = W = 9/4
The maximum area is:
A = 1 . 9/4
A = 9/4
A = 2.25
Answer: (30m-9n)/270
First we start with m/9-n/30.
We multiply the denominators to get 270.
Then we multiply the numerators by the original denominators to get (30m-9n).
To check, we can use m=2, and n=4
2/9-4/30=4/45
(30*2-9*4)/270=24/270=4/45
Let m and s be the number of math and sociology books sold respectively.
m=s+88 we are also told that:
m+s=426, using m found above in this equation gives you:
s+88+s=426 combine like terms on left side
2s+88=426 subtract 88 from both sides
2s=338 divide both sides by 2
s=169, since m=s+88
m=169+88=257
So 257 math and 169 sociology textbooks were sold.
Answer:
x = 2 y = 3
Step-by-step explanation:
