Here is our profit as a function of # of posters
p(x) =-10x² + 200x - 250
Here is our price per poster, as a function of the # of posters:
pr(x) = 20 - x
Since we want to find the optimum price and # of posters, let's plug our price function into our profit function, to find the optimum x, and then use that to find the optimum price:
p(x) = -10 (20-x)² + 200 (20 - x) - 250
p(x) = -10 (400 -40x + x²) + 4000 - 200x - 250
Take a look at our profit function. It is a normal trinomial square, with a negative sign on the squared term. This means the curve is a downward facing parabola, so our profit maximum will be the top of the curve.
By taking the derivative, we can find where p'(x) = 0 (where the slope of p(x) equals 0), to see where the top of profit function is.
p(x) = -4000 +400x -10x² + 4000 -200x -250
p'(x) = 400 - 20x -200
0 = 200 - 20x
20x = 200
x = 10
p'(x) = 0 at x=10. This is the peak of our profit function. To find the price per poster, plug x=10 into our price function:
price = 20 - x
price = 10
Now plug x=10 into our original profit function in order to find our maximum profit:
<span>p(x)= -10x^2 +200x -250
p(x) = -10 (10)</span>² +200 (10) - 250
<span>p(x) = -1000 + 2000 - 250
p(x) = 750
Correct answer is C)</span>
Answer:
the required answers are :
c) x = 2
d) x = 27 / 7
e) x = 9
f ) x = 6
Step-by-step explanation:
for explanation see the attached image
^_^
(-35-42-63)/7= (-140)/7=-20
To solve we need to use Pythagoras theorem (
)
There are 2 possible lengths for x: hypotenuse or one of the 2 shorter sides.
Hypotenuse:
10^{2} + 21^2 =
100+441=
23.3≈x
Shorter leg:
= 441-100
x≈18.47
Answer:
Height of the brick portion of the wall is 5.61 feet.
Step-by-step explanation:
Employees of the landscaping company used brick to build the top 2/3 of the wall. The total dimensions of the wall are 8 and 1/2 * 2 and 3/4 feet. So the height of the wall = 8 and 1/2 feet or in other words 8.75 feet.
Height of the brick portion of the wall = 2/3 * 8.5 = 0.66 * 8.5 = 5.61 feet
So the height of the brick portion of the wall is 5.61 feet.
Non brick portion of the wall is 8.5 - 5.61 = 2.89
