Answer: Number 1 is 40 dollars
Step-by-step explanation:
In order to find any of the info we need we have to find the first derivative of the equation. If

, then

. We are told to find the slope at point (1, 7). Using that x value in our derivative will give us the slope of the line at that point. y' = -(1)^2+8. So y' = 7. That's the slope of the line. Now we will use that slope along with the x and y coordinate in the slope-intercept form of a line to solve for b. 7 = 7(1) + b so b = 0. Our equation then is y = 7x. If you graph these in the same window on your calculator, you can see how perfectly that align at the given point. It's really quite perfect.
A,E,F
Sq rt of 25 is 5 and 5 is less than 10
Sq rt of 36 is 6 and 6 is less than 10
Sq rt of 9 is 3 and 3 is less than 10
Let the number be n.
Then:
n^2 + (1/n)^2 = 82/9; find n. Find the LCD; it is 9n^2.
Mult all 3 terms by 9n^2:
82*9n^2
9n^4 + 9 = (82/9)(9n^2) => 9n^4 + 9 = ------------
9
Then 9n^4 - 82n^2 + 9 = 0
I used my graphing calculator to find that n = 3.
Let's check: is 3^2 + (1/3)^2 = 82/9?
Is 9 + 1/9 = 82/9?
Is 81 + 1 = 82? YES. So, n=3 is a solution.