angelwings996
  • angelwings996
What is the solution of the equation? (x - 2)^3/4 = 8
Mathematics
schrodinger
  • schrodinger
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abb0t
  • abb0t
multiply by 4 and cube everything. then add 2 to solve for x.
angelwings996
  • angelwings996
\[(x - 2)^{3/4} = 8 \] is the equation
abb0t
  • abb0t
That's the same thing as: \[\sqrt[4]{a^3}\]

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angelwings996
  • angelwings996
@abb0t will there only be one solution?
anonymous
  • 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
anonymous
  • anonymous
This one won't have multiple solutions.
anonymous
  • anonymous
its like (x-2)^3 = 8^4 giving you x = 18. And only 1 root
angelwings996
  • angelwings996
@mominanisar Thanks!
angelwings996
  • angelwings996
Could any of you help me with one more please?
anonymous
  • anonymous
no problem
angelwings996
  • angelwings996
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?
angelwings996
  • angelwings996
@mominanisar @Saikam could either of you help me please?
angelwings996
  • angelwings996
It is multiple choice so I can list them
anonymous
  • anonymous
yes i will if i am able to
angelwings996
  • angelwings996
Okay, ill give you the choices
anonymous
  • 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
angelwings996
  • angelwings996
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.
angelwings996
  • angelwings996
@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
anonymous
  • anonymous
i agree with @Saikam
angelwings996
  • angelwings996
Then would I have to take an educated guess on this?
anonymous
  • 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?
angelwings996
  • angelwings996
Could you help me please?
jim_thompson5910
  • jim_thompson5910
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jim_thompson5910
  • jim_thompson5910
|dw:1358145052483:dw|
jim_thompson5910
  • jim_thompson5910
height of bridge above water = y coordinate of vertex length of the bridge above the arch = distance between the two roots
anonymous
  • 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
angelwings996
  • angelwings996
If you guys can't figure it out its okay(:
jim_thompson5910
  • jim_thompson5910
well it's implicit, they should state it more clearly though
jim_thompson5910
  • jim_thompson5910
y = height above the ground
jim_thompson5910
  • jim_thompson5910
or river, i meant
angelwings996
  • angelwings996
I agree...Ít's hard to do the math to something when you don't quite understand the question
anonymous
  • 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
angelwings996
  • angelwings996
So b?
anonymous
  • 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.
angelwings996
  • angelwings996
Lol its fine. I appreciate both of your helps! Thank you (:

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