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The easiest way to solve a simultaneous equation is by the method of substitution. First of all, we take the first equation, and rearrange it so that it is in terms of y. Or, in other words, rearrange it ...

sin cos -sin -cos (down is differentiate and up is integrate) so, y = sin5x  dy/dx = 5cos5x y=3cox      dy/dx = -3sinx y=3tan5x     dy/dx = 15sec²(5x) (remember sec(x) is the reciprocal of cos(...

Expand the brackets:

(3z + 18) - (8z + 2)

Simplify:

16 - 5z

Times both side by r to get ar+3r=2a+7 Subtract 2a and 3r from both side to bring a to one side, ar-2a=7-3r Factorise the left handside, a(r-2)=7-3r Divide both side by r-2, a=(7-3r)/(r-2)

The probability of picking a ball from a bag is the number of balls of that colour divided by the total number of balls.

Therefore in the first instance, the probability of a red ball is 3/9 or 1/3...