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Two fair six sided dice, called A and B, are rolled and the results are added together. The sum of the dice is 8, what is the probability that two fours were rolled?

We know that A+B = 8 so we should first count the number of ways that the two dice could total 8. (A = 2, B = 6), (A=3, B=5), (A=4, B=4), (A=5, B=3) , (A=6, B= 2) -- this gives 5 possible waysWe also know th...
JM
Answered by Jak M. • Maths tutor
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Find the turning point of y = x + 1 + 4/x2 and describe the nature of the turning point

To find the turning point of the equation, it should be recognised that we desire the point at which the gradient is 0. The gradient is given by dy/dx and hence we differentiate the equation with respect to ...
AK
Answered by Animit K. • Maths tutor
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Given y=2x(x^2-1)^5, show that dy/dx = g(x)(x^2-1)^4 where g(x) is a function to be determined.

y=2x(x 2 -1) 5 --> y=uv, where u=2x; v=(x 2 -1) 5 --> thus product rule required.u'=2v'=10x(x 2 -1) 4 Product rule: dy/dx = uv' + v'uTherefore: dy/dx = 2x(10x(x 2 -1) 4 ) + 2(x 2 -1) 5 g(x) = (22x 2 -2)
SH
Answered by Sean H. • Maths tutor
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Find the finite area enclosed between the curves y=x^2-5x+6 and y=4-x^2

Starting by factorising the curve equations: the first one factorises to y = (x-3)(x-2) and the second one becomes y=(2-x)(2+x). From this, a rough sketch of the curves can be drawn and it can be seen that f...
RN
Answered by Ruby N. • Maths tutor
4471 Views

Differentiate (3x^2-5x)/(4x^3+2x^2)

We can differentiate the expression using the quotient rule. If f(x)=u(x)/v(x) then f'(x)=(u'(x) v(x)-u(x) v'(x))/v(x)^2. In this case u(x)=3x^2-5x so u'(x)=6x-5 and v(x)=4x^3+2x^2 so v'(x)= 12x^2+4x. Using ...
AI
Answered by Andras Ivan A. • Maths tutor
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