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This is a word problem with the task of forming a first order differential equation (or DE), and involves two major aspects that need to be worked out: the volume of water in the tank at any given point, ...
The volume of revolution is given by integrating Piy2 dx from 0 to 1.Squaring, y2=1/(x2+2x+2)Completing the square, we see that y=1/((x+1)2+1)Make the subst...
is (2i + j) m/s. Find the shortest distance between P and Q in the subsequent motion. This is an m4 question from the edexcel June 2015 paper. First I would explain to the student that I would form an equ...
Substitute Cosh^2(x) = 1 + Sinh^2(x) into the starting equation (This formula should be known)Make 0 the subject 3Sinh^2(x) - Sinh(x) - 2 = 0Substitute u = Sinh(x) and solve for uSubstitute Sinh(x) back i...
Use the Taylor series expansion for the following three functions: f(θ) = e^(iθ), g(θ) = cos(θ) and h(θ) = sin(θ). We should find that f(θ) = e^(iθ) = 1 + iθ - (θ^2/2!) - i(θ^3/3!) + ... = Sum(θ^n/n!), g(...
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