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Maths
A Level

A curve is defined by the parametric equations x = 3 - 4t, and y = 1 + 2/t. Find dy/dx in terms of t.

At first glance, this looks quite tricky, as usually when we are asked to find dy/dx, we have one equation, but here we have 2.So in this case, we need to use the statement that dy/dx = (dy/dt) * (dt/dx)T...

WM
Answered by Wesley M. Maths tutor
10641 Views

What is the integral of (6x^2 + 2/x^2 + 5) with respect to x?

When we think of integration, we should be thinking of the same method every time; adding one to the power, and then dividing by that new power.The integral of the sum of each of these terms is equal to t...

WM
Answered by Wesley M. Maths tutor
8172 Views

How do you integrate (sinx)^2?

(sinx)^2 (similarly to (cosx)^2) cannot be integrated in this form. There is a standard method to get past this though, which makes use of the cos double angle formula:cos(2x) = (cosx)^2 - (sinx)^2       ...

WW
Answered by Will W. Maths tutor
39935 Views

Derive from the standard quadratic equation, the form of the quadratic solution

ax2+bx+c=0 : basic quadratic equation

a(x+ bx/a) + c=0  

a((x+b/2a)-

JD
Answered by Jaiveer D. Maths tutor
6266 Views

Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)

The first part is relatively simple.  If we write tan(3x) as tan(2x+x) we can use addition formulae to give:

tan(2x+x)= (tan(2x)+tan(x))/(1-tan(2x)tan(x))

tan(2x) = 2tan(x)/...

DG
Answered by Daniel G. Maths tutor
52888 Views

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