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butlerstown1
Manipulation of Formulae-Algebra

Please help me to solve: (1) Make x the subject of the formula z=3(y+x) (2) Make x the subject of the formula 2y = 1 - 4 3 x (3) If V = ax2 + b, express x in terms of V, a and b. (4) If V = πr2h find an expression for r. (5) If bd = n(2a + nd) find an expression for d. (6) If r = √x2 + y2 Find an expression for x. (7) If x + a = x + b Find an expression for x. C (8) Given that x = 3 and y = 3m2 . Express y in terms of x.


3 Comments
SeanKell
SeanKell
Best to explain this so you can do others in the future. Making X (or any other letter)the subject of a formula basically means your goal from the start is to isolate X (get it on it's own on one side of the = ). The rule is +numbers and letters changes to – as they move across the = and vice versa. Multiply to divide (divide are letters and numbers on the bottom of a fraction) move from top to bottom as they move across the = (this is cross-multiplication). Important : keep + and – numbers in brackets if you're cross multiplying them. If the letter is in brackets at the start you need to 'multiply it out' of the brackets. So ... z = 3(y+x) .... multiply out 3(y+x) to release x so 3multiplied by y + 3x Z = 3y + 3x ... +3y crosses over = to become – 3y Z – 3y = 3x ... the 3x means 3 multiplied by x, so the multiplied by 3 moves . across = to become Z –3y divided by 3 = x Z–3y = x couldn't draw the fraction line here but picture it over the 3 :) 3 If you want I can do video and post link as it's very hard to visualise all this in text only but in the meantime these might help, have a look at https://youtu.be/6cjqmu-Neog explains Cross-multiplication and https://youtu.be/9-3qs3Sh9a4 clever way of arranging if you have difficulty with these maths problems, Good Luck!
SeanKell
SeanKell
(3) V = ax2 + b need x on it's own so first move the +b V –b = ax2 ax2 means a multiplied by x multiplied by 2 V – b = x a and 2 crossed = to become V–b over a2 a2
SeanKell
SeanKell
(6) If r = √x2 + y2 Find an expression for x. r = √x2 + y2 .... Move y2 over to other side to become –y2 r – y2 = √x2 .... square both sides to remove √ and release x (r – y2) squared = x2 (squaring cancels-out the √ (r – y2) squared = x2 ....divide both sides by 2 (multiply by 2 moves over = to become ÷ 2 (r – y2) squared = x 2
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