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(a) In order to find the inverse of a function, it is easiest to swap x and y and solve for y. Here this would give, x=3y-5 => x+5=3y => (x+5)/3=y. Hence, f-1(x)=(x+5)/3. (b) Here it is important to...

The first step is to identify that the first equation is linear and the second equation is a quadratic as indicated by the x squared term. Next, take the first linear equation and substitute for y in the ...

The total area of the circle is pi*r^2 = 36 piThis means that the sector is 1/12th of a circle.A circle has 360 degrees and so the angle of the sector wil be 360/12 = 30 degrees.

Cos^2(x) + sin^2(x) = 1. Therefore Cos^2(x) = 1 - sin^2(x). So equation becomes 3Sin^2(x) + sin(x) + 8 = 9(1 - sin^2(x)). Then becomes 12sin^2(x) + sin(x) - 1This is quadratic equation, solved to (4sin(x)...

Equation 1 is 4x+5y=13 - multiply it by 3, Equation 2 is 3x-2y=27 - multiply it by 4, New equation 1 is 12x+15y=39, New eq...