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In the triangle ABC, AB = 16 cm, AC = 13 cm, angle ABC = 50 and angle BCA= x Find the two possible values for x, giving your answers to one decimal place.

Using the sine rule: sina/A = sinb/Bsinx/16 = sin50/13sinx = 16 * (sin50/13)sinx = 0.943x = 70.5 and 109.5
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Answered by Yva P. • Maths tutor
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Find the general solution of the differential equation: d^2x/dt^2 + 5dx/dt + 6x = 2cos(t) - sin(t)

First solve complementary function, i.e. d 2 x/dt 2 + 5dx/dt + 6x = 0. To do so, let x = e mt , where m = arbitrary constant. Differentiating gives dx/dt = m e mt and d 2 x/dt 2 = m 2 e mt . Substituting int...
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Answered by Mick G. • Maths tutor
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Using the product rule, differentiate: y = (x^2 - 1)(x^3 + 3).

y=(x 2 -1)(x 3 +3) let u=x 2 -1 u'=2x let v=x 3 +3 v'=3x 2 uv'+u'v=(x 2 -1)(3x 2 )+(2x)(x 3 +3) =(3x 4 -3x 2 )+(2x 4 +6X) = 5x 4 -3x 2 +6x
Answered by • Maths tutor
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integral of (tan(x))dx using the substitution u = cos(x)

given u = cos(x), therefore du/dx=-sin(x), as tan(x)=sin(x)/cos(x), can rewrite tan(x)=(-du/dx)/u, therefore integral can become [(-1/u)du], after inegrating you are left with -ln(u)+c, therefore ln(1/u)+c, ...
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Answered by Frederick R. • Maths tutor
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f(x) = x^x, find f'(3).

Therefore, y = x x can then natural log both sides leaving ln(y) = xln(x) then differentiating both sides wrst to x d/dx(ln(y)=xln(x))we are then left with this expression (dy/dx)(1/y)=ln(x)+1 multiplying up...
FR
Answered by Frederick R. • Maths tutor
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