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The velocity of a moving body is given by an equation v = 30 - 6t, where v - velocity in m/s, t - time in s. A) What is the acceleration a in m/s^2? B) Find the expression for the displacement s in terms of t given the initial displacement s(0)=10 m.

A) Acceleration is the rate of change of velocity with respect to time; therefore, in order to calculate it we need to differentiate the given equation of velocity v with respect to time t: a = dv / dt = d( ...
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Answered by Krisjanis P. • Maths tutor
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Integrate 5sinxcosx + 5cosx

*Use identity sinxcosx = 1/2sin2x =5/2sin2x + 5cosx *then use simple integration gives =(-5/2 x1/2)cosx + 5sinx + c = =5/4cosx +5sinx + c
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Answered by Joanne A. • Maths tutor
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Express (5-√ 8)(1+√ (2)) in the form a+b√2 , where a and b are integers

5 + 5√ 2 - √ 8 - √ 16 (Break up all terms in terms of square roots of 2) 5 + 5√ 2 - √ 8 - 4 5 + 5√ 2 - 2 √ 2 - 4 1 + 3√2
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Answered by Ignacio M. • Maths tutor
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Differentiate "sin(2x)"

Sinx differentiates to give cosx. We then multiply this by the differential of "2x." Which equals 2. Our answer therefore is "2cos(2x)."
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Answered by Ciaran B. • Maths tutor
10230 Views

Find the area between the curves y = x^2 and y = 4x - x^2.

First, we need to draw a diagram , to understand the question more clearly. y = x^2 is a common curve, but to sketch y = 4x - x^2, we should factorise it, to find where it inersects the x-axis. 4x - x^2 = x(...
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Answered by Lamisah M. • Maths tutor
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