What is the result when 8x^3+18x^2+11x+2 is divided by 2x+1

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:
p(x)= -10x^2 +200x -250
p(x) = -10 (10)² +200 (10) - 250
p(x) = -1000 + 2000 - 250
p(x) = 750

Correct answer is C)

7 0

3 years ago

Which function has a greater y-intercept?

Natali5045456 [20]

Answer:

Option C, both functions have an y-intersect equal to 2.

Step-by-step explanation:

When we have a function f(x), the y-intercept is the value f(0). This is the point where the graph of the function intersects the y-axis.

Then, for f(x) = -x^2 + 5*x + 2

The y-intercept is:

f(0) = -0^2 + 5*0 + 2 = 2

f(0) = 2

And for g(x) we do not have the equation, but we have the graph, so we can just look at which value of y does the graph intersects the y-axis.

We can see that the graph intersects the graph at y = 2

Then the y-intersect is: g(0) = 2

So both functions have the same y-intersect. Then the correct option is C.

4 0

3 years ago