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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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How can a volcanic eruption be predicted?

Constant monitoring of a volcano is crucial in being able to predict an upcoming eruption. Various technologies are used by volcanic monitoring stations, such as the Hawaiian Volcano Observatory, to detect c...
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Answered by Lydia P. • Geography 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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Translate the following: If it hadn't rained, she would have gone to the park.

S'il n'avait pas plu, elle serait allée au parc. Just as in the English example, this 'Si' clause requires the pluperfect tense and the conditional perfect. 'Si' clauses are constructed around two essential ...
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Answered by Milly L. • French tutor
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