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Integrate 10x(x^1/2 - 2)dx

First, expand the brackets. This will give us 10x^3/2 - 20x. Now to integrate this expression we have to increase the power of each term by one and then divide them by the number which becomes the new power....
GS
Answered by Giorgia S. • Maths tutor
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A curve has parametric equations -> x = 2cos(2t), y = 6sin(t). Find the gradient of the curve at t = π/3.

First we need to find the derivatives of x and y in terms of t. dx/dt can be found using the chain rule. Differentiating the inside of the bracket gives us 2. Multiplying the outside gives -2sin(2t) (Derivat...
MM
Answered by Matvei M. • Maths tutor
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How do I remember the common values of cosx, sinx and tanx?

To remeber the equations us SOH CAH TOA. This is Sinx = Opposite/Hypotenuse, Cos x = Adjacent/Hypotenuse and Tanx = Opposite/Adjacent. For values x=pi/3 and x=pi/6 always start by drawing an equilateral of s...
BL
Answered by Becky L. • Maths tutor
3805 Views

Let y be a function of x such that y=x^3 + (3/2)x^2-6x and y = f(x) . Find the coordinates of the stationary points .

y = x 3 + 1.5x 2 -6x Hence, dy/dx = 3x 2 + 3x - 6 Solve to find x when dy/dx = 0 as gradient is zero at stationary points Substitute the vaules for x back into y to find y coordinates of the stationary point...
MC
Answered by Michael C. • Maths tutor
4311 Views

Two forces P and Q act on a particle. The force P has magnitude 7 N and acts due north. The resultant of P and Q is a force of magnitude 10 N acting in a direction with bearing 120°. Find the magnitude of Q and the bearing of Q.

There are 2 methods to solving this- the visual method and the kinesthetic method. Here I will use the visual one. We start by creating a vector triangle. We are going to use R = P + Q, where R is the result...
YP
Answered by Yaasir P. • Maths tutor
12050 Views