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angelwings996

  • 2 years ago

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

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  1. abb0t
    • 2 years ago
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    multiply by 4 and cube everything. then add 2 to solve for x.

  2. angelwings996
    • 2 years ago
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    \[(x - 2)^{3/4} = 8 \] is the equation

  3. abb0t
    • 2 years ago
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    That's the same thing as: \[\sqrt[4]{a^3}\]

  4. angelwings996
    • 2 years ago
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    @abb0t will there only be one solution?

  5. mominanisar
    • 2 years ago
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    ((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. wio
    • 2 years ago
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    This one won't have multiple solutions.

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

  8. angelwings996
    • 2 years ago
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    @mominanisar Thanks!

  9. angelwings996
    • 2 years ago
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    Could any of you help me with one more please?

  10. mominanisar
    • 2 years ago
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    no problem

  11. angelwings996
    • 2 years ago
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    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. angelwings996
    • 2 years ago
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    @mominanisar @Saikam could either of you help me please?

  13. angelwings996
    • 2 years ago
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    It is multiple choice so I can list them

  14. mominanisar
    • 2 years ago
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    yes i will if i am able to

  15. angelwings996
    • 2 years ago
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    Okay, ill give you the choices

  16. Saikam
    • 2 years ago
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    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. angelwings996
    • 2 years ago
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    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. angelwings996
    • 2 years ago
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    @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. mominanisar
    • 2 years ago
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    i agree with @Saikam

  20. angelwings996
    • 2 years ago
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    Then would I have to take an educated guess on this?

  21. Saikam
    • 2 years ago
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    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. angelwings996
    • 2 years ago
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    Could you help me please?

  23. jim_thompson5910
    • 2 years ago
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    |dw:1358145028404:dw|

  24. jim_thompson5910
    • 2 years ago
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    |dw:1358145052483:dw|

  25. jim_thompson5910
    • 2 years ago
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    height of bridge above water = y coordinate of vertex length of the bridge above the arch = distance between the two roots

  26. Saikam
    • 2 years ago
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    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. angelwings996
    • 2 years ago
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    If you guys can't figure it out its okay(:

  28. jim_thompson5910
    • 2 years ago
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    well it's implicit, they should state it more clearly though

  29. jim_thompson5910
    • 2 years ago
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    y = height above the ground

  30. jim_thompson5910
    • 2 years ago
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    or river, i meant

  31. angelwings996
    • 2 years ago
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    I agree...Ít's hard to do the math to something when you don't quite understand the question

  32. Saikam
    • 2 years ago
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    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. angelwings996
    • 2 years ago
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    So b?

  34. Saikam
    • 2 years ago
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    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. angelwings996
    • 2 years ago
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    Lol its fine. I appreciate both of your helps! Thank you (:

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