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Express the following as a partial fraction: (4x^2+12x+9) / (x^2+3x+2) .

We first notice that the degree of the numerator is the same as the degree of the denominator so we have an improper fraction which we need to separate into an integer and a proper fraction before we can exp...
AP
Answered by Antonia P. • Maths tutor
5647 Views

What is the difference between the perfect tense and the imperfect tense?

Both tenses are used to describe something that happened in the past. In every day conversation, the perfect tense is almost always used e.g. j'ai joué, j'ai trouvé.... When writing, the perfect tense is use...
AC
Answered by Antoinette C. • French tutor
2410 Views

Explain why benzene is colourless whereas azo dyes (such as methyl yellow) are coloured.

Azo dyes are coloured because they contain alternating single and double bonds, known as a conjugated system. This creates and areas of delocalisation above and below the plane of the molecule. This area of ...
AS
Answered by Amy S. • Chemistry tutor
44142 Views

a) Find the general solution to the differential equation: f(x)=y''-12y'-13y=8. b) Given that when x=0, y=0 and y'=1, find the particular solution to f(x).

First consider y''-12y'-13y=0. Try: y=e mx . This gives y'=me mx and y''=m 2 e mx . Substituting into the differntial equation we get: m 2 e mx -12me mx -13e mx =0 Since e mx >0 divide throughout by e mx ...
AP
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How do I write the function 3cosθ+4sinθ in the form Rsin(θ + α), where R and α are positive constants?

Split it up into steps: Step 1: Use compound angle trigonometric formula to re-write Rsin(θ + α) Since generally sin(θ ± φ) = sinθcosφ ± cosθsinφ Rsin(θ + α) = R(sinθcosα + cosθsinα) = Rsinθcosα + Rcosθsinα ...
OG
Answered by Oliver G. • Maths tutor
12956 Views