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 height is 36 in
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a rectangular based pyramid.
Step one
Given data
Volume v = 1944 in
length of base l = 18 in
width of base w = 9 in
Height h= ?
Step two
we know that the expression for the volume of a pyramid is given as
substituting our given data we have
but volume = 1944 in therefore
Answer:
y = 0
Step-by-step explanation:
Simplifying
0.1y = 15y
Solving
0.1y = 15y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-15y' to each side of the equation.
0.1y + -15y = 15y + -15y
Combine like terms: 0.1y + -15y = -14.9y
-14.9y = 15y + -15y
Combine like terms: 15y + -15y = 0
-14.9y = 0
Divide each side by '-14.9'.
y = 0
Simplifying
y = 0
X+6. An expression does not have an equal sign.
2.4x = 8.4.....divide both sides by -2.4
x = 8.4/-2.4
x = - 3.5