Search over 10,000 free study notes

First solve for the exact point on the line by substituting 5 into the original equation. You should get y=+-4. 
Now implicitly differentiate the equation: 4x-6y(dy/dx)=0. Rearranging this will yiel...

We know in a quadratic x^2 +bx + c = 0, -b/a = α + β and c/a = αβ. 

Therefore, α + β = -(-2k) = 2k, and αβ = k - 1. (Both are divided by the coefficient in front of x which is 1 so can be ignored.<...

P- (3,0) y=ln(x/3)     u=x/3    y=ln(u) ​​​​​​            du = 1/3  dy = 1/u = 3            dx       du dy= du x dy dx dx  du   = 1/3 x 3 = 1 gradient at normal = -1 equ...

£45.00

x=3,y=2