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two balls of similar size masses m and 2m are moving at speeds u and 2u along a frictionless plane, they collide head on and are reflected, assuming that the coefficient of restitution of this collision is 1, what the speeds are afterwards in u

ball A has mass m and velocity u. ball B has mass 2 m and velocity 2uby conservation of momentum:mu - 4mu = mv + 2mx (1)where v is the velocity of ball A and x is the velocity of ball B after collision.by co...
WA
Answered by William A. • Maths tutor
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An ordinary, fair sided dice is rolled 480 times. How many times is the number 3 expected?

An ordinary dice has six sides. We have an equal chance to roll on any of these six sides. This gives us the probability of rolling a 3 (or any other number) as 1/6.Each roll is independent i.e the result of...
LP
Answered by Louis P. • Maths tutor
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How do I solve a quadratic equation: x^2-5x+6=0

When solving a quadratic equation, you have two options. Take the general form ax^2+bx+c=0Method 1: Solution by FactorisingWhen the numbers involved look fairly simple, look for a way to factorise the quadra...
NC
Answered by Naomi C. • Maths tutor
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Expand and Simplify: (x+2)(x+3)(x−3)

(x+2)(x+3)(x−3)(x 2 + 3x + 2x + 6)(x - 3) : Step 1 is to expand the first two brackets. (x 2 + 5x + 6)(x - 3) : Step two is to simplify the quadratic. x 3 -3x 2 +5x 2 -15x+6x-18 : Then expand the quadratic w...
AH
Answered by Alex H. • Maths tutor
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Let n be an integer greater than 1. Prove that n^2 - 2 - (n-2)^2 is an even number.

To show a number N is even, we must be able to express it in the form N = 2x for some other whole number x. Let's try to manipulate the given expression to see if we can put it in this form. By expanding the...
SL
Answered by Sam L. • Maths tutor
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