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Solve the quadratic equation x^2 + x - 6 = 0

There are 3 methods for solving quadratic equations;FactorisingThe quadratic equationCompleting the SquareUsing method 1,We observe that 2 and 3 are factors of 6 and that 3 - 2 = 1 so by factoring out we hav...
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Answered by Thomas A. • Maths tutor
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Find the integral of ln(x)

The best way to approach this question is to solve it using integration by parts.First, recognise that ln(x) = 1 x ln(x), and set du/dx = 1 and v = ln(x). We then find that u = x, and dv/dx = 1/x.With this w...
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Answered by Finn G. • Maths tutor
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The cost of a ticket increases by 10% to £19.25. What is the original cost?

The best way to approach this question is by solving it algebraically. By constructing an equation that links the original cost to the current cost (let original cost be X), this would give you X*(1+10%) = 1...
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Answered by Robin L. • Maths tutor
13982 Views

Prove by induction that 7^(8n+3) + 2 is divisible by 5, where n is a natural number.

We need to first consider the base case, n=0. (We consider the smallest possible value of n as the base case.)7^(8 0+3) + 2 = 343 + 2 = 345 = 69 * 5, so the statement is true for n=0. Assume true for n = k, ...
MP
Answered by Mingke P. • Maths tutor
6948 Views

Amber has an unfair coin. The probability of throwing a tail is p. Amber throws the coin twice and the probability of throwing a head and then a tail is 6/25. Heads are more likely than tails. Show that 25p^2-25p+6=0 and find the value of p.

Tree diagramP(Head then tail) = p(1-p)=6/25Solve above equationp=2/5 as heads are more likely than tails.
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Answered by Muhammed S. • Maths tutor
3206 Views