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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
4054 Views

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) = ...
HX
Answered by Henry X. • Maths tutor
16783 Views

log_10⁡((1/(2√2))*(p+2q))=(1/2)(log_10⁡p+log_10⁡q),p,q>0,find p in terms of q.

log 10 [(1/2√2) (p+2q)]=(1/2)(log 10 p+log 10 q)log 10 [(1/2√2) (p+2q)]=(1/2)(log 10 pq)log 10 [(1/2√2) (p+2q)]=log 10 (pq) 1/2 (1/2√2) (p+2q)=(pq) 1/2 (p+2q) 2 =8pqp 2 +4pq+4q 2 =8pqp 2 -4pq+4q 2 =0(p-2q)=0...
HX
Answered by Henry X. • Maths tutor
9185 Views

Find the integral of 4/(1-x^2) dx:

The first thing to notice here is that the denominator of the integrand is a case of 'difference of two squares'. The integral, which I will call I, can be rewritten as the integral of 4/((1+x)(1-x)) dx. If ...
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Answered by Jemima P. • Maths tutor
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