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To solve this problem we will use a clever substitution to easily integrate and thus obtain the answer.First we can represent tan(x) as its fractional equivalent sin(x)/cos(x), assigning the variable u to...

First, we need to remove one of the variables from one of the equations. In this case, we multiply the first equation by 4 to give 12x+4y=28.Then minus the 2nd equation from this to give 10x+0y=20.Now div...

Take a right angled triangle with hypotenuse of length 1, and angle at the bottom of the hypotenuse equal to x. We will let o denote the length of the side opposite the angle, and a denote the length of t...

The first step is to find dx/dy in terms of y, which when differentiating comes out as 3/2cos(y/2), so dy/dx in terms of y is the reciprocal of this.The next step is to eliminate the y dependent terms, wh...

dy/dx = 6x^1/2 + 2 y = (62/3)x^3/2 + 2x + c = 4x^3/2 + 2x + c 38 = (416^3/2) + (2*16) + c c = 38 - 256 - 32 = -250 y = 4x^3/2 + 2x - 250