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Solving 2tan(x) - 3sin(x) = 0 for -pi ≤ x < pi

The first step to answering this question is to get the equation in a simpler form. Aim to have it solely in terms of sin(x) and cos(x) with no fractional parts. To begin doing this, remember that tan(x) = s...
BA
Answered by Benjamin A. • Maths tutor
21906 Views

Take the polynomial p(x)=x^4+x^3+2x^2+4x-8, use the factor theorem to write p(x) as two linear factors and an irreducible quadratic. An irreducible quadratic is a quadratic that can not be factorised.

We must use the factor theorem since that is what the question asks. So we take p(x) and think about the factors of 8 we then evaluate it at x=1 to start, then move onto x=-1,2,-2 and so on. We see that it h...
JC
Answered by Jordan C. • Maths tutor
4639 Views

How would the integral ∫x^2sin2xdx be solved using integration by parts?

The general formula for integration by parts is given as ∫u(dv/dx)dx = uv - ∫v(du/dx)dx given that the equation to be solved is ∫x 2 sin2xdx, the values for u, v, du/dx and dv/dx can be assigned as u = x 2 d...
SN
Answered by Samuel N. • Maths tutor
11472 Views

A stone is thrown from a bridge 10m above water at 30ms^-1 30 degrees above the horizontal. How long does the stone take to strike the water? What is its horizontal displacement at this time?

The first thing to do for part a) is work out the vertical component of the velocity. By drawing a triangle where 30m/s is the hypotenuse with angles of 30 degrees, 90 degrees, and 60 degrees, and by applyin...
SU
Answered by Sarah U. • Maths tutor
6361 Views

What is the derivative of f(x)=sqrt(3x+2)=(3x+2)^(1/2)?

By the power rule, the derivative of x^(n) is nx(n^1) and by the chain rule, the derivative of g(h(x)) is g'(h(x))h'(x). Let g(x)=x^(1/2) and h(x)=3x+2 so that f(x)=g(h(x)). Then by the power rule, g'(x)=(1/...
LP
Answered by Luke P. • Maths tutor
5521 Views