How do you solve #H=(J^3)/(CD) - (K^3)/D# for J?

Answer 1

Rearrange using arithmetic operations to separate #J^3# on one side of an equation, then take cube roots to get:

#J = root(3)(HCD+K^3C)#

First add #K^3/D# to both sides to get:
#H + K^3/D = J^3/(CD)#
Multiply both sides by #CD# to get:
#HCD + K^3C = J^3#

Take the cube root of both sides to get:

#J = root(3)(HCD+K^3C)#

This assumes Real arithmetic. If dealing with Complex numbers there would be two additional possible solutions:

#J = omega root(3)(HCD+K^3C)#
#J = omega^2 root(3)(HCD+K^3C)#
where #omega = -1/2 + sqrt(3)/2i#
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Answer 2

To solve for ( J ), first, multiply both sides of the equation by ( CD ) to get rid of the denominators. Then, move the terms involving ( J ) to one side of the equation and the constant terms to the other side. Finally, divide both sides by ( H ) and take the cube root to isolate ( J ). The formula would be:

[ J = \sqrt[3]{\frac{HCD - K^3D}{C}} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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