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This exercise will help you rearrange some complex equations.

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Rearrange the following equations in the given variable .

For more help, check this video - https://www.youtube.com/watch?v=eTSVTTg_QZ4

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To rearrange any formula or equation, follow these easy steps:

1.Start by multiplying both sides by the denominator.

2. Cancel out the like terms on either side of equation.

3. Now expand out the brackets.

4. Then collect the like terms on one side and the given subject on same side.

5. Now you can factorise/solve using BIDMAS to get the answer in the given variable

Example: In part a)

1.Start by multiplying both sides by the denominator

for example if you have $V=\\frac{\\var{a}S}{S+ \\var{b}}$ then multiply both sides by $(S+ \\var{b})$

2.This gives: $V(S+ \\var{b})=\\frac{\\var{a}S}{S+ \\var{b}} (S+ \\var{b}) $

the $({ S+ \\var{b}})$ term on the right hand side cancels out to give: $V(S+ \\var{b})= \\var{a}S$

3. Now expand out the brackets: $VS+\\var{b}V= \\var{a}S$

4. Then collect the like terms, you want to get all the terms with S in them onto one side, so subtract VS from both sides:

$VS-VS+ \\var{b}V=\\var{a}S-VS$

This becomes $\\var{b}V=\\var{a}S-VS$

5. Now you can factorise the right hand side: $\\var{b}V=S(\\var{a}-V)$

6. Then divide both sides by $({\\var{a} -V})$ to leave S on its own: $\\frac{\\var{b}V}{\\var{a}-V}=S$

For more help, check this video-

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Rearrange the following equation to make S the subject.

$ V=\\frac{\\var{a}S}{S+\\var{b}}$

Note: To write a fraction you type (numerator)/(denominator)

S=[[0]]

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To transpose or rearrange a formula you may:

add or subtract the same quantity to or from both sides
multiply or divide both sides by the same quantity
square or square root both sides
Expand out brackets or simplify using BIDMAS

Example: if y = x + 8,

subtracting 8 yields

y − 8 = x + 8 − 8

y − 8 = x, thus changing the subject to X

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Rearrange the equation by making 2 as the subject:

$A=\\frac{bh}{2}$

To transpose or rearrange a formula you may:

add or subtract the same quantity to or from both sides
multiply or divide both sides by the same quantity

1.In this part, take the denominator to the other side and

2.Divide the right hand side by A to get equation making 2 the subject

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$2=\\frac{bh}{A}$

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$2=\\frac{A}{bh}$

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2= $A$ - $bh$

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2= $A$ + $bh$

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Rearrange the equation by making 'g' the subject of the formula:

$\\displaystyle{\\frac{(f-\\var{i})^2}{(\\var{g}+\\var{i})}}=\\var{x}$

$g=\\;$ [[0]]

Note: To write a fraction, use (nominator)/ (denominator) and to square use '^2' sign

1.Start by multiplying both sides by the denominator.

2. Cancel out the like terms on either side of equation.

3. Now expand out the brackets.

4. Then collect the like terms on one side and the given subject on same side.

5. Now you can factorise/solve using BIDMAS to get the answer in the given variable

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Rearrange the formula to make 'a' the subject:

$\\ s =\\ u{t} + \\frac {\\var{r}}{\\var{k}} at^2$

$a=\\;$ [[0]]

Note: To write a fraction, use (nominator)/ (denominator) and to square use '^2' sign

1.Start by taking the different variables to the other side, in this case - ut

2. Multiply the other side by 2 to cancel 2 from right side of equation.

3. Now divide the whole term by t^2 to get the equation in terms of a.

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Rearrange the following in terms of L:

$\\ t =\\var{k}\\var{p} \\sqrt\\frac{L}{g}$

$L=\\;$ [[0]]

Note: To write a fraction, use (nominator)/ (denominator) and to square use '^2' sign

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1. Multiply both sides to square the root term.

2. Now take different variables to the other side

3. Get the equation in terms of L.

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Rearrange the following to make $v$ the subject:

$\\ K = \\frac {\\var{r}}{\\var{k}} m(v^2-u^2)$

$v=\\;$ [[0]]

Note: To write a term in square root, use sqrt(term)

1. Take the denominator 2 to the other side of equation

2. Divide the other side by m ( the nominator in the right side)

3. Take u^2 to other side and change signs

4. Square root the whole left side to get the answer in terms of v

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