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Solve the equation 2log (base 3)(x) - log (base 3)(x+4) = 2

First express as a single logarithm as follows. The number in front of the logarithm remembering log rules can be rewritten as the power of the number in the bracketsSo rewriting the LHS
log₃

Answered by Theranjit S. • Maths tutor

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Show that the set of real diagonal (n by n) matrices (with non-zero diagonal elements) represent a group under matrix multiplication

We must show that the set satisfies the group requirements: Identity, Closure, Associativity and Invertibility.Identity: Contains identity matrixAssociativity: Follows from the rules of matrix multiplicat...

Answered by Nishil P. • Further Mathematics tutor

2673 Views

solve the simultaneous equations: 3x + 5y = 4 ; 7x - 3y = 8

first recognise that if you double the first equation the both equations will be equal to 8.so now we have 6x + 10y = 8 ; 7x - 3y = 8now we can set the equations equal to each other to get 6x + 10y = 7...

Answered by Elizabeth W. • Maths tutor

3960 Views

differentiate: y=[xcos(x^3)]/[(x^4 + 1)^3] with respect to x

This question is on the trickier side as it is heavily computational and requires a good knowledge of the differentiation rules however it is a good way to practise using multiple rules at once.First we w...

Answered by Elizabeth W. • Maths tutor

2715 Views

Find the volume of a right angled triangular prism with an angle of 28 degrees, hypotenuse of length 10 cm, and projected length of 12.5 cm. Give your answer in cm^3, to three significant figures.

The area of a prism is found by multiplying the area of the end face by the projected length. The adjacent and opposite side lengths of the triangle can be found using SOHCAHTOA. sin(28)= opposite/10, the...

Answered by Lily M. • Maths tutor

3308 Views