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Express 4sin(x)+6cos(x) in terms of Rsin(x+a) where R and a are constants to be determined (a should be given in rad).

R=sqrt(42)=6.48...a=arcos(4/sqrt(42))=0.905...Rsin(x+a)=6.48sin(x+0.905)

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Integrate ln(x)

Take ln(x) = 1 * ln(x) and integrate by parts. Let u = ln(x) and dv/dx = 1 such that du/dx = 1/x and v = x. Using the integrating by parts formula, you get x ln(x) - integral(1) = x ln(x) - x + c.

Answered by Jason Y. • Maths tutor

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A ball of mass m moves towards a ball of mass km with speed u. The coefficient of restitution is 0. What is the final velocity if the first ball after the collision.

Coefficient of restitution is defined as the ratio of the relative speed of separation of the balls to the relative speed of approach. A ratio of 0 means that the speed of separation has a value of zero a...

Answered by Susannah E. • Maths tutor

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Differentiate cos^2(x)

Using the chain rule, Let y=cos²(x)Let u=cos(x)y=u²dy/du=2udu/dx=-sin(x)dy/dx=dy/du*du/dx=-2sin(x)cos(x)

Answered by Manish B. • Maths tutor

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Find the equation of the tangent to the curve x^3+yx^2=1 at the point (1,0).

We can find the gradient of a tangent to a curve at a point by finding dy/dx at x=1.Firstly we can rearrange the equation of the curve for y.(1) yx^2=1-x^3(2)y=x^{-2}-xThen we can differentiate the equati...

Answered by Ollie G. • Maths tutor

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