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Every complex number has a real and imaginary part. For the complex number z=a+bi the notation for real and imaginary parts respectively are Re(z)=a and Im(z)=b. If you know thi...

Using the implicit form derivative rule: y'=-F_x' / F_y' :

y'=-(2 x sin(x+y)+x² cos(x+y)-5 y e^x) / (x² cos(x+y)-5 e^x)

Degrees are a made up unit; mathematicians simply decided that a complete revolution of a circle has 360 degrees, without that number actually meaning anything. Tecnically any number could have been picke...

Using the method of binomial expansion (which I will cover in more detail) we get

(2x-3y)^4 = + 1(2x)^4(3y)^0  -  4(2x)^3(3y)^1  +  6(2x)^2(3y)^2  -  4(2x)^1(3y)^3  +  1(2x)^0(3y)^4  =

= 16x...

Draw a rough sketch of the graph of f(x) = sin(x-1) to get an idea of what the region looks like. Realise that the normal volume of revolution for the area between x axis and the f(x) is given by V = pi* ...