tangent line, derivative, graph question free response style calculus AB hepp!!?

Question

1 Line L is tangent to the graph of y=x-(x^2/500)
on the graph, L crosses y axis at (0, 20)
point Q is on the both graph of y=x-(x^2/500) and the tangent line L.

(a) Find the x-coordinate of point Q.

(b) Write an equation for line l in slope-intercept form.

(c) Suppose the graph of y=x-(x^2/500) shown in the figure, where x and y are measured in feet, represents a hill.
There is a 50-foot tree growing vertically at the top of the hill. Does a spotlight at point P directed along line l
shine on any part of the tree? Show the work that leads to your conclusion.

**** and would you please be accurate and show details?? cuz i am not smart enough... :((****

Answer 1

slope = dy/dx =m = 1- x/250
The equation of the line L is y=.6x +20
Set .6x+20=x-x^2/500
300x +10,000 =500x -x^2
x^2 -200x +10,000 =0
x = 100
So Point Q is at (100, 80)

I have no clue where Point P is so have no way of answering your final question.

Answer 2

a million. discover the spinoff of your function, y'=3x^2 2. you ought to use your spinoff function to discover the slope or value of substitute as long as you have an x fee. it rather is what you ought to make sure, the x fee. 3. Use your equation of the line to discover that is slope. ( y = 3x + a million), for the reason that's in slope intercept variety, it rather is EZ, the slope or value of substitute is 3. 4. Set your spinoff equation equivalent to 3 and resolve for x. i'm getting plus/minus a million. this potential you have 2 x values to evaluate. 5. discover the standards on your curve (y = x^3), i'm getting (a million,a million) and (-a million, -a million) 6. you recognize the slope of the tangent lines are the two 3 (must be to be parallel to the line given). 7. Now make sure the eqauation of the lines employing the factor and slope, i could advise employing pt. slope variety for a line. y - y1=m(x - x1) 8. For one among you ideas: y -a million=3(x-a million) the different could be y+a million=3(x+a million) 9. in case you have a graphing calculator, you ought to make sure that the solutions on your lines make experience too. good success! S-Dawg