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

- angelwings996

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

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- abb0t

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

- angelwings996

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

- abb0t

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

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## More answers

- angelwings996

@abb0t will there only be one solution?

- 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

This one won't have multiple solutions.

- anonymous

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

- angelwings996

@mominanisar Thanks!

- angelwings996

Could any of you help me with one more please?

- anonymous

no problem

- 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

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

- angelwings996

It is multiple choice so I can list them

- anonymous

yes i will if i am able to

- angelwings996

Okay, ill give you the choices

- 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

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

@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

i agree with @Saikam

- angelwings996

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

- 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

Could you help me please?

- jim_thompson5910

|dw:1358145028404:dw|

- jim_thompson5910

|dw:1358145052483:dw|

- jim_thompson5910

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

- 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

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

- jim_thompson5910

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

- jim_thompson5910

y = height above the ground

- jim_thompson5910

or river, i meant

- angelwings996

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

- 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

So b?

- 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

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

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