Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

How the hell to make x the subject?

*pic below*

could someone please tell me how to make x the subject? I've been trying for ages. Trying to make dA/dx = 0 so only the top part = 0 and just stuck

OP

any help is appreciated

Is that the whole question?

Study Forum Helper

Original post by zezno

*pic below*

could someone please tell me how to make x the subject? I've been trying for ages. Trying to make dA/dx = 0 so only the top part = 0 and just stuck

Original post by zezno

any help is appreciated

What's the actual question?? Sure you can make the differential equal 0 to find the points where

A

is minimised/maximised.

In which case you have

48x^2+x(x^2-50)\sqrt{100-x^2}-2400=0

\Leftrightarrow 48x^2-2400 = -x(x^2-50)\sqrt{100-x^2}

and note that

48x^2-2400=48(x^2-50)

then carry on from there.

(edited 7 years ago)

OP

Original post by RDKGames

What's the actual question?? Sure you can make the differential equal 0 to find the points where

A

is minimised/maximised.

In which case you have

48x^2+x(x^2-50)\sqrt{100-x^2}-2400=0

\Leftrightarrow 48x^2-2400 = -x(x^2-50)\sqrt{100-x^2}

and note that

48x^2-2400=48(x^2-50)

then carry on from there.

I always get stuck when there's more than 1 x term with powers involved.

So I noticed that you can cancel out the (x^2 -50) which gave me:

-x(100-x^2)^1/2 = 48

I tried getting rid of the square root so now:

-x(100-x^2) = 2304

expanding

-100x + x^3 = 2304

and yeah stuck lol two x's, factorising would give me though:

x(-100+x^2) = 2304

Study Forum Helper

Original post by zezno

I always get stuck when there's more than 1 x term with powers involved.
...

I tried getting rid of the square root so now:

-x(100-x^2) = 2304

...

This should be

x^2(100-x^2)=2304

OP

Original post by RDKGames

This should be

x^2(100-x^2)=2304

ah okay. Then what next?

Study Forum Helper

Original post by zezno

ah okay. Then what next?

Achieve the form

x^4+bx^2+c=0

then you have a quartic which you can treat as a quadratic with a simple substitution

X=x^2

and solve for

X

by solving the quadratic then solve for

x

itself.

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