Answer:
S'(x)=-0.006x2+0.8x+9
Step-by-step explanation:
The rate of change of the sales S(x) with respect to the amount of money spent on advertising x is then the derivative of S(x) with respect to x. What we have to calculate is S'(x).
We know that the derivative of 
is 
(where a is a constant), and the derivative of a sum is the sum of the derivatives, so we can calculate the derivative of each term independently:
S'(x)=(−0.002x3 + 0.4x2 + 9x + 500)'=(−0.002)(3)x2 + (0.4)(2)x + 9
Which means:
S'(x)=-0.006x2+0.8x+9
Answer: (1, 2)
Concept:
There are three general ways to solve systems of equations:
- Elimination
- Substitution
- Graphing
Since the question has specific requirements, we are going to use <u>elimination</u>
Solve:
<u>Given expressions</u>
x + 5y = 11
-x + 4y = 7
<u>Add both equations together to elimination [x] variable</u>
(x + 5y) + (-x + 4y) = 11 + 7
x - x + 5y + 4y = 18
9y = 18
<u>Divide 9 on both sides</u>
9y / 9 = 18 / 9
<u>Find the x value</u>
x + 5y = 11 ⇔ <em>Given equation</em>
x + 5(2) = 11 ⇔ <em>Substitute values of y</em>
x + 10 = 11 ⇔ <em>Simplify by multiplication</em>
x + 10 - 10 = 11 - 10 ⇔ <em>Subtract 10 on both sides</em>
Hope this helps!! :)
Please let me know if you have any questions
C is the answer hope this helps.
