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solve for x, in the form x = loga/logb for 2^(4x - 1) = 3^(5-2x) (taken from OCR June 2014 C2)

We can take logs of both sides straight away, and using the log rule that alogb = log(b^a)So(4x-1) log(2) = (5 - 2x) log(3)We can expand the bracketsso (4x)log(2) - log(2) = 5log(3) - 2xlog(3)We can group th...
EN
Answered by Ellie N. • Maths tutor
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Find the eigenvalues and eigenvectors of A = ([2, 0 , 0], [0, 1, 1], [0, 3, 3])

We can use the characteristic equation, det(A - k I) = 0 to find the eigenvalues of A. Performing this, we see that(2-k) * ( (1-k) (3-k) - 3 ) = 0.Immediately, we can see a root is k = 2, which is our first ...
CT
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Discuss how the cardiovascular system adapts to long term aerobic exercise.

In response to aerobic exercise (longer durations at a lower intensity using oxygen), the cardiovascular (CV) system adapts over time to become more efficient. Adaptions include cardiac hypotrophy where the ...
AJ
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Calculate y=4x-6 when x=3

Firstly we have an equation y=4x-6. We are given that x=3 and we want to find y. What we must do is substitute x=3 into the equation to get y: y=4(3)-6 =6
SU
Answered by Sinan U. • Maths tutor
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Expand and simplify (3x^2 + 2)(2x + 5) – 6x(x^2 – 3)

First, multiply out 6x(x^2 - 3) so that it becomes – 6x^2 – 18xThen, multiply (3x^2 + 2) and (2x + 5) so that it becomes 6x^3 + 15x^2 + 4x + 10Add the two results above: 6x^3 + 15x^2 + 4x + 10 – 6x^3 – 18x S...
AB
Answered by Ancel B. • Maths tutor
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