Answer:
55
Step-by-step explanation:
12 x 5 = 60
60-5 = 55
55 is not prime
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:
x=36
Step-by-step explanation:
First rewrite equation then multiply each side by 36. 9x-36=4x+144.
then move the variable 9x-4x+36=144. Next subtract 9x and 4x ...5x=144+36.... 5x=180. Lastly you divide 180÷5 this your answer x=36
Volume of the cone is 117.5 π ft³
<u>Step-by-step explanation:</u>
Lateral area of the cone = πrs
s is the slant height = 15 ft
From the above formula, we can find the radius as, 5 ft.
Volume of the cone = π r² h/3
s = √ (5²+ h²)
Squaring on both sides, we will get,
s² = 15² = (5² + h²)
15² - 5² = h²
225 - 25 = 200 = h²
h = √200 = 14.1 ft
Volume = π × 5² × 14.1 / 3 = 117.5 π ft³
Let's solve :
a.) The equation will be :
b.) the table will be like this :
point (1 , -3)
point (3, -1)
point (-1 , 3)
point (-3 , 1)
c.) graph the equation as shown in attachment !
