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Maths
A Level

A particle of mass 0.25 kg is moving with velocity (3i + 7j) m s–1, when it receives the impulse (5i – 3j) N s. Find the speed of the particle immediately after the impulse.

In order to answer this question, we must first understand the concept of impulse. When a force acts on an object, its momentum is being changed, and this change is defined as the impulse. Put simply, Imp...

AM
Answered by Aashish M. Maths tutor
7867 Views

The quadratic equation 2x^2 + 6x + 7 = 0 has roots A and B. Write down the value of A + B and the value of AB

Upon being told to find the roots of a quadratic we should investigate the various different ways of finding these roots. With experience you will learn to be able to find roots without many calculations ...

KD
Answered by Killian D. Maths tutor
9170 Views

Find dy/dx of y = a^x

To differentiate a function of the form y=a^x you need to use a neat little trick to rewrite a^x in the form of something you already know how to differentiate. Using the fact that e^ln(x) is equal to x, ...

TD
Answered by Tutor33284 D. Maths tutor
23457 Views

Show how '2sin(x)+sec(x+ π/6)=0' can be expressed as √3sin(x)cos(x)+cos^2(x)=0.

To do this question we must first be aware of a few trigonometric identities. 1. sec(x) = 1/cos(x). 2. cos(A + B) = cos(A)cos(B) - sin(A)sin(B). (double angle formula) 3 . sin^2(x) = 1 - cos^2(x) Before d...

RP
Answered by Ruadhan P. Maths tutor
9828 Views

How do you find the integral of 'x sin(2x) dx'?

To begin, notice that the expression involves 2 functions of x multiplied together, this means we can approach the problem using integration by parts. Integration by parts can be expressed as '∫ u (dv/dx)...

RP
Answered by Ruadhan P. Maths tutor
22055 Views

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