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log_a(36) - log_a(4) = 0.5, what is a?

This is an example of a question you might face during a higher maths examination. It is also a great question to test what your understanding of logarithms and powers are. I have given a quick explanation b...
NA
Answered by Nasir A. • Maths tutor
1409 Views

Point K(8,-5) lies on the circle x^2 +y^2 - 12x - 6y - 23. find the equation of the tangent at K.

First, find the centre of the circle. Since we know the equation of the circle, we know that the centre (-g,-f) comes from the part of the equation -12x-6y, where -12=2g and -6=2f. Therefore, to get the cent...
CM
Answered by Catriona M. • Maths tutor
2748 Views

Calculate the rate of change of d(t )=2/(3t), t ≠ 0, when t=6.

When a question asks for rate of change, this means you need to differentiate the equation. First you need to put the equation into differentiable a form ie, with the no variables on the denominator: f(t) = ...
LI
Answered by Lucy I. • Maths tutor
2671 Views

How do I find the dot product of two 3-dimensional vectors

Example; Let vector v = (2,5,2) and vector u = (1,-2,3),then u · v = [(2 x 1) + (5 x -2) + (2 x 3)] = [2 -10 + 6] = -2 As the workings hopefully make clear in the line above, the general formula for the scal...
TV
Answered by Theo V. • Maths tutor
1574 Views

Solve log_2(3x + 7) = 3 + log_2(x – 1), x > 1.

Begin by collecting log_2 terms.log_2(3x + 7) - log_2(x – 1) + = 3 Using the rule of log terms we getlog_2((3x+7)/(x-1)) = 3 (3x+7)/(x-1) = 2 3 3x+7 = 8(x-1)3x+7-8x+8 = 0 -5x+15 = 0 x= 3
CF
Answered by Catriona F. • Maths tutor
2592 Views