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Integrate (3x^2 - (1/4)x^-2 + 3) dx

3x 2 -(1/4)x -2 +3 Split the problem into three separate terms and integrate independently.With any term where x is to the power of something, divide the coefficient by the value of the power plus 1 .e.g. 3x...
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Answered by Lucy L. Maths tutor
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What is 4536000 in words and what is that number to 3 significant figures?

In words: four million five hundred and thirty six thousand 3 S.F : 4540000
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Answered by Billy W. Maths tutor
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Solve to find x: 32x + 43 = -8x - 17

In order to find 'x', one must be able to isolate x on one side of the equation. This would be achieved firstly by adding +8x to both side of the equation:The left hand side would thus look like this: 40x + ...
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Answered by Francis B. Maths tutor
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Katie buys: 3 pens costing £2.20 each, 1 rubber costing £1.60 and 2 pencils. She pays with a £10 note and a £2 coin. She gets 20p change. What was the price of each pencil?

You can put this question into the form of an equation in order to solve it.Step 1: The total cost of the items is (10+2)-0.20= £11.80. Step 2: putting it in equation form: let x be the price of 1 pencil, we...
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Answered by Juliette W. Maths tutor
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Prove by mathematical induction that (2C2)+(3C2)+(4C2)+...+(n-1C2) = (nC3).

Firstly, show the equation is true for n = 3 (as this is the samllest n that nC3 is defined): LHS = (2C2) = 1 = (3C3) = RHStherefore, true for n=3. Then assume true for n = k:(2C2)+(3C2)+(4C2)+...+(k-1C2) = ...
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Answered by Henry X. Maths tutor
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