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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
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Calculate the distance of the centre of mass from AB and ALIH of the uniform lamina.

The diagram shows the lamina shape. To begin, divide the lamina into smaller sections and calculate the area. In this example, the lamina is best divided into sections A, B and C. Calculate the areas. For ex...
CS
Answered by Chandler S. • Maths tutor
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What is the equation for photosynthesis and what is the product used for?

Equation: carbon dioxide + water ---(with light energy)---> glucose + oxygen Glucose is the important product of the photosynthesis reaction. Some of the glucose is used in respiration to provide energy f...
IR
Answered by Isabelle R. • Biology tutor
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How do I begin to analyse an unseen text?

The answer is simple and this structure can be applied to any type of text, irresective of the genre or length: Reading, reflecting and responding. Reading: At the beginning of the examination, the priority ...
SG
Answered by Sorana G. • English tutor
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