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Find the indefinite integral tan(5x)tan(3x)tan(2x)

Noticing that tan(5x) = tan(3x+2x) we use the tan compound angle formula to find tan(5x) = (tan(2x)+tan(3x))/(1-tan(2x)tan(3x)) and thus tan(5x)tan(3x)tan(2x) = tan(5x)-tan(3x)-tan(2x). From then we can inte...
SO
Answered by Sean O. • Maths tutor
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What is a Tierce de Picardie?

A Tierce de Picarie ('Picardy Third') is a surprise major chord at the end of a piece. Whilst the piece is predominantly in a minor mode, the final chord (which will always be the tonic in music of this peri...
HW
Answered by Harriet W. • Music tutor
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Factorise (x^2 +3x-18)=0, solving for x

To factorise and solve this equation we must put it into two brackets, instead of one, each with a single x term. As the is an x^2 term we know there must be an x in each bracket Because the number term at t...
RM
Answered by Rachael M. • Maths tutor
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Solve for simultaneous equations x +5y =9 and 3x + 2y =5.

Here we have 2 unknown variables, x and y. First number the two equations, so x + 5y = 9 is (1), while 3x + 2y = 5 (2). Rearrange both equations so that they become (1) x = 9-5y and (2) x= (5-2y)/3. Next, si...
AL
Answered by Abigail L. • Maths tutor
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How to do you create subjunctive in the present tense?

First of all take the word in the infinitive (e.g. comer/ hablar/ vivir) Then put conjugate it into the first person singular (e.g. como, hablo, vivo). Then take off the "o" ending. If it is an er/...
AJ
Answered by Alice J. • Spanish tutor
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