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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 ...

Factorising basically means put whatever equation you are given into brackets. So, E.g. x² + xFirst you want to look for a common factor which here is X. Therefore, the answer would be x(x+1).T...

Total journey average speed = (total distance travelled ÷ total time taken).Total distance travelled = 213 miles + 37 miles = 250 milesTotal time taken (hours) = 4 + (50÷...

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

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(...