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What's the gradient of the curve y=x^3+2x^2 at the point where x=2?

Gradient is change in y divided change in x.As the change shrinks to effectively nothing (as we want to gradient at a point, not between points), we use dy/dx (the derivative of y with respect to x), to work...
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Answered by Zachary I. • Maths tutor
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Solve the simultaneous equations: y = x + 6, x^2 + 2y = 9

y = x + 3x 2 + 2y = 9We want to make the squared equation have either only x's or only y's, so we substitute y = x + 3 into the equation:x 2 + 2(x + 3) = 9We need to take out the brackets, and simplify this ...
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Answered by Hayley H. • Maths tutor
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How do I write a personal statement for Oxbridge?

Oxbridge personal statements differ from many other universities, in that they are looking for a more academic personal statement. Whilst other universities might be interested in your extra-curricular activ...
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When should I use the subjunctive?

In Spanish, there are 3 modes: indicative, subjunctive and imperative. We are going to be looking the first two of these. The indicative is probably the mode that you are most familiar with, and is used for ...
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Answered by Kyra L. • Spanish tutor
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Prove by induction that, for n ∈ Z⁺ , [3 , -2 ; 2 , -1]ⁿ = [2n+1 , -2n ; 2n , 1-2n]

STEP 1: Prove that the theorem holds for n = 1. Substitute n = 1 into the equation and show that the LHS = RHS. STEP 2: Assume that the relation is true when n = k. STEP 3: Prove that the relation holds for ...
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Answered by Flavia T. • Maths tutor
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