## anonymous 3 years ago What is the solution of the equation? (x - 2)^3/4 = 8

1. abb0t

multiply by 4 and cube everything. then add 2 to solve for x.

2. anonymous

$(x - 2)^{3/4} = 8$ is the equation

3. abb0t

That's the same thing as: $\sqrt[4]{a^3}$

4. anonymous

@abb0t will there only be one solution?

5. anonymous

((x - 2)^1/4)^3 = 8 =2^3 it powers are same then you can compare the bases i.e (x - 2)^1/4 = 2 then multiply the both sides with ^4 then you will get x-2=16 x=18

6. anonymous

This one won't have multiple solutions.

7. anonymous

its like (x-2)^3 = 8^4 giving you x = 18. And only 1 root

8. anonymous

@mominanisar Thanks!

9. anonymous

Could any of you help me with one more please?

10. anonymous

no problem

11. anonymous

You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y = -0.000471x^2 + .837x where x and y are measured in feet. How high above the river is the bridge (the top of the arch)? Hw long is the section of bridge above the arch?

12. anonymous

@mominanisar @Saikam could either of you help me please?

13. anonymous

It is multiple choice so I can list them

14. anonymous

yes i will if i am able to

15. anonymous

Okay, ill give you the choices

16. anonymous

actaully, the length of the section of bridge and its height above the river are dependant on each other. one cannot be determined without the other

17. anonymous

a. The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. b. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 1,777.07 ft. c. The bridge is about 371.85 ft. above the river, and the length of the bridge above the arch is about 888.54 ft. d. The bridge is about 1,777.07 ft. above the river, and the length of the bridge above the arch is about 371.85 ft.

18. anonymous

@Saikam That's what everyone is saying, so Im not able to find the answer anywhere. Im not even sure how you would figure this out

19. anonymous

i agree with @Saikam

20. anonymous

Then would I have to take an educated guess on this?

21. anonymous

no. we must consider each option and verify. take the length of bridge given in the first option, then check if it satisfies the given height. Then take the values from second option, and so on... one (or more) of them might satisfy. can u try? or u want me to help?

22. anonymous

23. jim_thompson5910

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24. jim_thompson5910

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25. jim_thompson5910

height of bridge above water = y coordinate of vertex length of the bridge above the arch = distance between the two roots

26. anonymous

No @jim_thompson5910 because the question doesnt say that the x-axis is the level of the river. it could be anything. like y=1, y=-1 , etc.that is why the verification needed

27. anonymous

If you guys can't figure it out its okay(:

28. jim_thompson5910

well it's implicit, they should state it more clearly though

29. jim_thompson5910

y = height above the ground

30. jim_thompson5910

or river, i meant

31. anonymous

I agree...Ít's hard to do the math to something when you don't quite understand the question

32. anonymous

dy/dx = 0 gives you the x-xoordinate, where the arch has its vertex 0 = -0.000942 x + 0.837 2x = 0.837/0.000471 This could be equated to length of the river 2x = 1000*(837/471) = 1777.07 ft for which the only option matching is b :P

33. anonymous

So b?

34. anonymous

you should substitute this value of x (x, and not 2x )in the equation and check for y . If its equal to 371.85, then yea, B. I just woke up. feeling lazy to do the calculations.

35. anonymous

Lol its fine. I appreciate both of your helps! Thank you (: