We are given coordinates of the school located at a point (9,-1).
Library is located 5 blocks south and 4 blocks west .
According to coordinate axes, south is downward and west is on left side.
So, we need to move 5 units down of 9.
<em>5 units down of 9 would be 9-5 = 4.</em>
And then <em>4 blocks west that mean -1 -4 = -5.</em>
<h3>Therefore, coordinate of the library is located at the point (4,-5).</h3>
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:
-3
Step-by-step explanation:
Numbers that come out of the absolute values are always positive.
|6 - 4| -|3 - 8| =
| 2| - | -5| =
2 - 5 =
-3
The maximum number of roots to a polynomial of order n is n roots. Take the example of a quadratic (order 2) which can intersect the x-axis a maximum of 2 times, and similarly a cubic (order 3) 3 times maximum.
Hence for 8 intersections, minimum order = 8
