## anonymous one year ago Kitaer is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 2 hours. Kaitlyn can complete the project in 1 hours. Kitaer wants to know how long it will take them to complete the project together.

1. anonymous

really confused on this?

2. anonymous

@jim_thompson5910

3. jim_thompson5910

x = time it takes for Cody to do the job alone y = time it takes for Kaitlyn to do the job alone z = time it take them to do the job together we're given x = 8 and y = 6. Solve for z $\large \frac{1}{x}+\frac{1}{y}=\frac{1}{z}$ $\large \frac{1}{8}+\frac{1}{6}=\frac{1}{z}$ $\large \frac{3}{24}+\frac{4}{24}=\frac{1}{z}$ $\large \frac{3+4}{24}=\frac{1}{z}$ I'll let you finish

4. anonymous

so 5/24?

5. jim_thompson5910

no

6. anonymous

7. jim_thompson5910

$\large \frac{3+4}{24}=\frac{1}{z}$ $\large \frac{7}{24}=\frac{1}{z}$ cross multiply or take the reciprocal of both sides

8. anonymous

Oh! Okay :) Sorry, I didn't notice that

9. anonymous

so 7z=24

10. anonymous

yes?

11. jim_thompson5910

now fully isolate z

12. anonymous

13. jim_thompson5910

14. anonymous

is that the answer?

15. anonymous

16. jim_thompson5910

17. anonymous

Thanks :)

18. jim_thompson5910

what are some key features that you can think of? any at all?

19. anonymous

Maybe some degrees?

20. jim_thompson5910

you mean the degree of the polynomial?

21. anonymous

yes

22. jim_thompson5910

what does the degree tell us?

23. anonymous

how many answers it would have

24. anonymous

I mean roots

25. jim_thompson5910

close, the degree tells us the maximum number of roots, or x-intercepts, possible example: x^3 + 7x^2 + 9 has at most 3 roots. It could have 3 roots, or 2 roots, or just 1 root.

26. anonymous

I understand. :)

27. jim_thompson5910

the degree also tells us how many turning points there are number of turning points = (degree) - 1 example: degree = 3 means we have 2 turning points |dw:1437527865525:dw|

28. jim_thompson5910

also, a degree 3 polynomial has 3 branches |dw:1437527902361:dw|

29. jim_thompson5910

other key features: * y intercept * end behavior

30. jim_thompson5910

the end behavior is explained in these articles http://www.purplemath.com/modules/polyends.htm http://www.mathwords.com/e/end_behavior.htm

31. anonymous

Ok! Thank-you<3 So the answer would be

32. anonymous

basically we need degress, y-intercepts, and end behaviors

33. jim_thompson5910

knowing the degrees helps us determine how many roots max are possible it doesn't tell us the actual x-intercepts

34. jim_thompson5910

you have to set the polynomial equal to 0 and solve for x

35. jim_thompson5910

key features used to graph: x-intercepts y-intercept number of turning points (equal to degree - 1) end behavior also, a couple of other points doesn't hurt either

36. anonymous

Hahha :) Thanks !

37. jim_thompson5910

np