Answer:
$3
Step-by-step explanation:
Given that:
p = 8 - ln(x) when 5 < x < 500
where;
x = The total number of dogs sold
Then;
The total revenue = x * p
R = x(8 - ln(x))
R = 8x - xln(x)
The Company thus pays 1 dollar per dog
i.e.
The total cost C = 1 * x = x
Then: Profit = R - C
P = 8x - xln(x) - x
P = 7x - xln(x)
Differentiating P in respect to x
dP/dx = 7 - d/dx(xln(x))
dP/dx = 7 - x*d/dx(ln(x)) - ln(x)*d/dx(x)
dP/dx = 7 - x(1/x) - ln(x)
dP/dx = 6 - ln(x)
Since this must be maximized, dP/dx is set to be equal to 0
6 - ln(x) = 0
ln(x) = 6
x = e^6
Now, p = 8 - ln(x)
Plug in the value of x :
p = 8 - ln(e^5)
p = 8 - 5
p = 3
Therefore, each dog must be priced at $3 to maximize the profit.
Answer:
The age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years.
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
Step-by-step explanation:
Current age of Alex = 8
Current age of the horse in human years = 50
Since the age of the horse is already stated in human years, it implies there is no need to convert the age of the horse again.
Therefore, since Alex is a human who was born 8 years ago, the age of the horse, in human years, when Alex was born can be determined by simply deducting the Current age of Alex from the Current age of the horse in human years as follows:
The age of the horse, in human years, when Alex was born = 50 - 8 = 42
Therefore, the age of the horse, in human years, when Alex was born was 42 years.
This can be presented in a table as follows:
Age of Alex Age of the Horse (in human years)
Eight years ago 0 42
Current age 8 50
Answer:
1-7i
Step-by-step explanation:
Multiply the parenthesis
-3-4i-3i-4i²
By Definition i²=-1
-3-4i-3i-4 x (-1)
Any expression multiplied by -1 equals its opposite
-3-4i-3i+4
Calculate the sum
1-4i-3i
Collect like terms
1-7i
Yes, this can happen if the rectangles are the same dimensions, BUT NO if the dimensions are different.
Answer:
100
Step-by-step explanation:
