The product of the sum of two perfect cubes:
a³ + b³ = (a + b)(a² - ab + b²)
The product of the difference of two perfect cubes:
a³ - b³ = (a - b)(a² + ab + b²)
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Remember to follow FOIL:
(b^2 + 8)(b^2 - 8)
(b^2)(b^2) = b^4
(b^2)(-8) = -8b^2
(8)(b^2) = 8b^2
(8)(-8) = -64
b^4 - 8b^2 + 8b^2 - 64
Combine like terms:
b^4 (-8b^2 + 8b^2) - 64
b^4 - 64
b^4 - 64 is your answer
hope this helps
Answer:
<em>The minimum average cost is $2.80 when 163 players are built</em>
Step-by-step explanation:
<u>Average Cost Function</u>
<em>We'll assume the given function as the total cost to produce x players, and NOT the average cost since that is a different definition, as shown below.</em>
The cost C to produce x DVD/Blu- ray players is given by the equation
The Average Cost function is defined as
To find the extreme value of the average cost, we must take the first derivative of the function
Equating to 0
Solving for x
The second derivative is
For x=163 the second derivative is positive, thus x=163 is a minimum value. Let's compute the minimum average cost
The minimum average cost is $2.80
Answer:
Step-by-step explanation:
Given
Required
Determine the interval which it belongs
The given number is less than 1
i.e.
And it is greater than 0.
So, the number is located between 0 and 1
i.e.
Problem 1.
Think of the outer rectangle by joining the two 5 in. sides with a segment.
Now you have an outer blue rectangle with a white rectangle missing.
For the outer rectangle:
The top and bottom sides measure 28 in.
The left and right sides measure 5 in. + 12 in. + 5 in. = 22 in.
Area of the outer rectangle = LW = 28 in. * 22 in. = 616 in.^2
Now look at the white square. You need to subtract this area from the outer rectangle.
area of white rectangle = LW = 12 in. * 15 in. = 180 in.^2
Subtract the areas:
616 in.^2 - 180 in.^2 = 436 in.^2
Answer:
<span>A. 436 Square Inches
Problem 2.
Do the same thing as for problem 1. Join the two 4 in. segments with a line.
</span>
<span>Think of the outer rectangle by joining the two 4 in. sides with a segment.
Now you have an outer blue rectangle with a white rectangle missing.
For the outer rectangle:
The top and bottom sides measure 24 in.
The left and right sides measure 4 in. + 12 in. + 4 in. = 20 in.
Area of the outer rectangle = LW = 24 in. * 20 in. = 480 in.^2
Now look at the white square. You need to subtract this area from the outer rectangle.
area of white rectangle = LW = 12 in. * 13 in. = 156 in.^2
Subtract the areas:
480 in.^2 - 156 in.^2 = 324 in.^2
Answer:
</span><span>B. 324 Square Inches</span>
