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If 2 log(x + a) = log(16a^6), where a is a positive constant, find x in terms of a

Use the power rule on the right hand side of the equation to reduce the expression into simpler termsRemoves logs (several methods, I would personally halve and then cancel)Factorise to give x=a(4a^2<...

Answered by Michael L. • Maths tutor

3786 Views

A graph is given with a plot of y = sin(x) for 0 <= x <= 360. Which value of x in the range 90 <= x <= 180 satisfies sin(x) = sin(30)?

x = 150.This question requires that the student uses the symmetry of the sine graph. If we draw y = sin(30) on top of y = sin(x), it is clear that a possible value of x is 150.
A harder question coul...

Answered by Jake S. • Maths tutor

8754 Views

A right angled triangle has two smaller sides length 3 and 4, what is the length of its longest side?

As we are told it is a right angled triangle we known that we can use Pythagoras's formula of c² = a²+b² given that we have been given lengths of 3 and 4 we simply substit...

Answered by Benjamin G. • Maths tutor

2379 Views

Integrate sin^2(x) with respect to x

use trigonometric identities i.e. Cos(2x) = Cos²(x) - Sin²(x) (a) Cos²(x) + Sin²(x) = 1 (b)Therefore: Cos²(x) = 1 - Sin²

Answered by Oscar L. • Maths tutor

3207 Views

Given that 2cos(x+50)°=sin(x+40)° show tan x° = tan 40°/3

The formulae for the sum the sine and cosine of two angles are: 2(cos x°cos 50°- sin x°sin 50°)= sin x°cos 40°+cos x°sin 40°cos 50°= sin 40°sin 50° = cos 40° Therefore, 2 cos x°sin 40°- 2 sin x°cos 40° = ...

Answered by Prashasti T. • Maths tutor

6645 Views