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Solve the simultaneous equations: y = x + 6, x^2 + 2y = 9

y = x + 3x² + 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:x² + 2(x + 3) = 9We need to take out the brack...

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 ac...

Answered by Hayley H. • Personal Statements tutor

1903 Views

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 f...

Answered by Kyra L. • Spanish tutor

1601 Views

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 relat...

Answered by Flavia T. • Maths tutor

5288 Views

A particle P of mass 2 kg is held at rest in equilibrium on a rough plan. The plane is inclined to the horizontal at an angle of 20°. Find the coefficient of friction between P and the plane.

For any mechanics question such as this one the best way to start off is by drawing a diagram of the system and including all the forces acting on the pa...

Answered by Fernando B. • Maths tutor

5656 Views