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What is differentiation

Differentiation is a mathematical operation which we can use to study how one quantity, such as the distance travelled by a train, is affected by another quantity, such as time. For example, if the train is ...
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Answered by Oliver B. • Maths tutor
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How do you factorise?

Factorising basically means put whatever equation you are given into brackets. So, E.g. x 2 + xFirst you want to look for a common factor which here is X. Therefore, the answer would be x(x+1).To check this ...
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Answered by Lydia D. • Maths tutor
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Johnny take 4 hours 50 minutes to drive 213 miles to Manchester. He then takes the train to Liverpool. Liverpool is 37 miles from Manchester and the train travels at 90mph. Calculate Johnny's average speed for his total journey in mph.

Total journey average speed = (total distance travelled ÷ total time taken).Total distance travelled = 213 miles + 37 miles = 250 milesTotal time taken (hours) = 4 + (50 ÷ 60) + time from Manchester to Liver...
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Answered by Steven W. • Maths tutor
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What is the derivative of y = (3x-2)^1/2 ?

Use the chain rule, u = 3x-2dy/dx = dy/du du/dxdy/du = d(u^1/2)/du = 1/2 u ^-1/2power down and minus 1du/dx = 3constants =0so, dy/dx = 3 1/2 (3x-2)^-1/2= 3/2 (3x-2)^-1/2
CJ
Answered by Chloe J. • Maths tutor
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Write 5cos(theta) – 2sin(theta) in the form Rcos(theta + alpha), where R and alpha are constants, R > 0 and 0 <=alpha < 2 π Give the exact value of R and give the value of alpha in radians to 3 decimal places.

Use the formula cos(A+B)=cosAcosB-sinAsinB, Rcos(theta+alpha)=Rcos(alpha)cos(theta)-Rsin(alpha)sin(theta)5=Rcos(alpha)2=Rsin(alpha)tan(alpha)=2/5alpha= 0.381R=sqrt(5^2+2^2)=sqrt(29)So, 5cos(theta) – 2sin(the...
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Answered by Joe W. • Maths tutor
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