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There are 10 beads in a bag. Four beads are green, six are black. If three beads are taken at random without replacement, what is the probability that they are the same colour?

There are two possible outcomes in which all beads are the same colour: they may be all green, or all black. We need to work out the probability of each outcome to start with. This is done by multiplying tog...
TW
Answered by Tom W. • Maths tutor
5178 Views

The curve C has equation y=(2x-3)^5, the point P lies on C and has coordinates (w, – 32), find (a) the value of w and (b) the equation of the tangent to C at the point P in the form y=mx+c , where m and c are constants.

(a) The curve is defined by y=(2x-3)^5. To find x=w when y=-32, we must substitute these values into the equation C and re-arrange to find w. -32=(2w-3)^5. First we must remove the power of 5 by doing power ...
JP
Answered by Jordan P. • Maths tutor
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The equation of the line L1 is y = 3x – 2. The equation of the line L2 is 3y – 9x + 5 = 0. Show that these two lines are parallel.

The equation of a straight line is usually given in the form y = mx + c. To prove that two lines are parallel we will need to show that both lines have the same gradient. The gradient of a line is the slope/...
TK
Answered by Tanya K. • Maths tutor
4942 Views

Find the volume of revolution when the curve defined by y=xe^(2x) is rotated 2*pi radians about the x-axis between x=0 and x=1

This is a standard question that may be found in a C4 mathematics paper. Students should use knowledge of the volume of revolution formula V = pi int_{a}^{b} y 2 dx to find the expression V = pi int_{0}^{1} ...
HS
Answered by Hanish S. • Maths tutor
4164 Views

How should I approach a proof by induction question?

Proof by induction is a powerful proof technique that can be used to prove a certain property and is a common question on the IB exams. Consider for instance the problem "Prove that sinx + sin3x +...+ s...
AR
Answered by Aditya R. • Maths tutor
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