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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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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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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 particle P. In order to do so, we have to account for th...
FB
Answered by Fernando B. • Maths tutor
7039 Views

A curve has the equation y=3 + x^2 -2x^3. Find the two stationary points of this curve.

At stationary point the derivative of y with respect to x equals zero. Find dy/dx. dy/dx = 2x - 6x 2. Set dy/dx = 0 ,giving 2x - 6x 2 = 0. We can rearrange this to x(1-3x) = 0 and solve the equation for x. T...
TC
Answered by Thomas C. • Maths tutor
4911 Views

Find the derivative of the following function: f(x) = x(x^3 + 2x)

f(x) becomes f'(x)1) First multiply out the brackets (by adding the indices) = x^4 + 2x^22) Then differentiate this. The indices moves to the front and multiplied by the number before the x. The indices is t...
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Answered by Shamailla S. • Maths tutor
3576 Views