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When working with probabilities why is it sometimes necessary to add and sometimes to multiply?

Whether you need to add or multiply depends on whether it is a case of 'AND' or 'OR'. For 'AND' you multiply, and for 'OR' you add. Below are examples of each case, using dice as an example: To calculate the...
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Answered by Marcus W. • Maths tutor
3461 Views

Solve the simultaneous equations: y=x^2 + 3x + 7 and y=x + 10

x= -3 and 1y= 7 and 11
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Answered by Usmaan S. • Maths tutor
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Differentiate the following equation: f(x) = 5x^3 + 6x^2 - 12x + 4

Answer: f'(x) = 15x^2 + 12x -12 This is according to basic rules of differentiation and is a beginner level differentiation question as following:If f(x) = ax^nThen f'(x) = x(nx^n-1)
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Answered by Holly K. • Maths tutor
3467 Views

Differentiate 5x^3 + 4x^2 + 5x + 9

Differentiate 5x 3 + 4x 2 + 5x + 9The rules from polynomial differentiation: d(ax n ) / dx= a(nx n-1 ) and df/dx + dg/dx = d (f+g) /dx and dn/dx = 0Using these rules in conjunction we get : 5(3x 3-1 ) + 4(2x...
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Answered by Annabelle S. • Maths tutor
4138 Views

A curve has equation 3x^4/3-16y^3/4=32. By differentiating implicitly find dy/dx in terms of x and y. Hence find the gradient of the curve at the point (8,1).

3x 4/3 -16y 3/4 =32Differentiating implicitly:4x 1/3 -12y -1/4 (dy/dx)=0Simplifying and rearranging:x 1/3 =3y -1/4 (dy/dx)dy/dx=1/3(x 1/3 y 1/4 ) Finding dy/dx using the (x,y) co-ordinates given:dy/dx=1/3(8 ...
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Answered by Ben G. • Maths tutor
3986 Views