Answer:
Step-by-step explanation:
Answer:
I don't see the polygon but all you need to do is add up all the sides.
The questions for this problem would be:
1. What is the dimensions of the box that has the maximum volume?
2. What is the maximum volume of the box?
Volume of a rectangular box = length x width x height
From the problem statement,
length = 12 - 2x
width = 9 - 2x
height = x
where x is the height of the box or the side of the equal squares from each corner and turning up the sides
V = (12-2x) (9-2x) (x)
V = (12 - 2x) (9x - 2x^2)
V = 108x - 24x^2 -18x^2 + 4x^3
V = 4x^3 - 42x^2 + 108x
To maximize the volume, we differentiate the expression of the volume and equate it to zero.
V = 4x^3 - 42x^2 + 108x
dV/dx = 12x^2 - 84x + 108
12x^2 - 84x + 108 = 0x^2 - 7x + 9 = 0
Solving for x,
x1 = 5.30 ; Volume = -11.872 (cannot be negative)
x2 = 1.70 ; Volume = 81.872
So, the answers are as follows:
1. What is the dimensions of the box that has the maximum volume?
length = 12 - 2x = 8.60
width = 9 - 2x = 5.60
height = x = 1.70
2. What is the maximum volume of the box?
Volume = 81.872
<h3>
Answer: B) y = -x</h3>
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Work Shown:
g(x) = x^2-2
g(-2) = (-2)^2-2
g(-2) = 2
Saying (-2, g(-2)) is the same as saying (-2, 2)
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g(x) = x^2-2
g(1) = 1^2 - 2
g(1) = -1
Saying (1, g(1)) is the same as saying (1, -1)
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Let's find the slope of the line through (-2,2) and (1,-1)
m = (y2 - y1)/(x2 - x1)
m = (-1-2)/(1-(-2))
m = (-1-2)/(1+2)
m = -3/3
m = -1
Now turn to point slope form to find the equation
y - y1 = m(x - x1)
y - 2 = -1(x - (-2))
y - 2 = -(x + 2)
y - 2 = -x - 2
y-2+2 = -x-2+2 ... add 2 to both sides
y = -x
You could use the other point (1,-1) and you'd get the same answer. The slope m = -1 is the same each time.
See the picture attached (excuse the cheesy drawing skills)
T means Tails, H means Heads
