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Differentiate the following: 3/2 x^(3/4) + 1/3 x^(-1/4)

In simple differentiation, we can use the fact that if y= x^n, dy/dx is equal to nx^(n-1). In other words, multiply the x term by the power, then decrease the power by 1. Here we have 2 terms so approach the...
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Answered by Alex W. • Maths tutor
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Find the Lowest common multiple of 96 and 132

First, split into prime factors- 96= 2^5 * 3 and 132= 2^2 * 3 * 11 Whilst very similar to highest common factor, lowest common multiple is found by comparing the two sets of prime factors, and for each prime...
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Answered by Alex W. • Maths tutor
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There are n sweets in a bag, 6 of which are orange. If the probablility of eating 2 orange sweets from the bag, one after the other, is 1/3, show that n^2 - n - 90 = 0. State any assumptions made.

We are assuming that the sweets are selected at random. The question says that the sweets are eaten, so we are also assuming that they aren't put back into the bag. The total probability of selecting the two...
JB
Answered by James B. • Maths tutor
4395 Views

Give an example of a real-world system that would be described by a quadratic equation. Explain the significance of the two real roots, a repeated root, and undefined roots. Is there any significance to a positive or a negative answer in your example?

For a ball that has been thrown, it's height above the ground can be described by a quadratic equation of the time since it was thrown and gives a parabola. The two real roots of the equation are the times w...
JB
Answered by James B. • Maths tutor
4610 Views

How can i use completing the square to factorise and solve equations

This method will only work if your x term is divisible by 2. For example x 2 + 6x + 12. You then use the halved x term (e.g. 3x) to complete the square. The beginning of your factorisation is now (x + 3) 2 ....
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Answered by Natalie S. • Maths tutor
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