What is the following product
1 answer:
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Answer:
Step-by-step explanation:
Given the function:
To find:
Domain of the function.
Solution:
First of all, let us learn about definition of domain of a function.
Domain of a function is the valid input values that can be provided to the function for which output is defined.
OR
Domain of a function are the values of
for which the output
is a valid value.
i.e. The function does not tend to or does not have
form.
So, we will check for the values of for which
is not defined.
For value to tend to , denominator will be 0.
So, the domain can not have x = 2
Any other value of x does not have any undefined value for the function .
Hence, the answer is:
[2 is not included in the domain].
Answer:
$4800
Step-by-step explanation:
The cost is minimized when any pair of opposite faces of the box costs the same as any other pair. Since the top+bottom total $25 per square foot and the sides (left+right or front+back) total $20 per square foot, the area of a side must be 25/20 = 5/4 times the area of the top or bottom.
If we let x represent the length of one side of the square bottom, then 5/4x will be the height of the box. Its volume will be ...
(5/4x)(x²) = 640 ft³
x³ = (4/5)(640 ft³) = 512 ft³ . . . . . . multiply by 4/5
x = 8 ft . . . . . . . . . . . . . . . . . . . . . . . take the cube root
The base area is then (8 ft)² = 64 ft², and the cost of the top+bottom is ...
64 ft² × $25/ft² = $1600
The three pairs of opposite sides will cost 3×$1600 = $4800.
The minimum cost of the constructed box is $4800.
_____
You can also write an equation for the total cost in terms of x, the side length of the base. That cost function will be ...
c(x) = 15x² + 10x² + 10·4x(640/x²)
This simplifies to ...
c(x) = 25x² +25600/x
A graph shows the minimum is c(8) = 4800 (as above).
__
Algebraically, you can set the derivative to zero to find the value of x.
dc/dx = 0 = 50x -25600/x²
512 = x³ . . . . multiply by x²/50 and add 512
8 = x . . . . . . . take the square root. Same solution as above. <em>Cost is minimized when the side length of the base is 8 ft</em>.
