Hockey Kenny

I can solve it using a graphing calculator but I need a solution method for my math tool belt.

Thanks in advance.

I need y = <Something> from this:

77.76/x²y - .9y = 151.56

Or even y² = something would work.

Is it possible?

For the Equation f(x,y) = 300/xy what are the partial derivates with respect to x and y.

I come up with -300/x²y and -300/y²x respectively. Is that correct?

Need to solve using Partial Derivatives:

Original Equation:

5xz + 5yz + 3xy + 2z + x + y

We know that xyz must equal 400

So I got started by solving for z with the third equation.

z = 400/xy

Substituted back into the original equation:

5x(400/xy) + 5y(400/xy) + 3xy + 2(400/xy) + x + y

Simplified:

2000/y + 2000/x + 3xy + 800/xy + x + y

Took Partials with respect to x and y (are my partials for 800/xy correct?)

fx = -2000/x² + 3y - 800/x²y + 1

fy = -2000/y² + 3x - 800/xy² + 1

Now I need where fx and fx = 0 for max/min.

0 = -2000/x² + 3y - 800/x²y + 1

This is where I get lost.

10 points on the line!!!

4 Unknowns, 4 Equations. Actually solving using a LaGrange Multiplier (r=lamba). Everytime I try solving for a different unknown, it gets very complex. There must be a trick for solving this.

2y + z + 4 = yzr

2z + x + 3 = xzr

2y + 2x + 2 = xyr

xyz = 100

Integrate:

√(3-2Cos(4t))

or, if this is easier, integrate:

√(4Sin²(2t) + 1)

They come from arc length question with parametric equation: Cos(2t)i + tj

I know that the derivative of e^x is e^x. I need to show that using the definition of a derivative (D = Delta):

f'(x) = (f(x+Dx) - f(x))/Dx

I use (e^(x+Dx) - e^x)Dx and I get

((e^x)(e^Dx) - e^x)/Dx

or

(((e^x)(e^Dx))/e^x)/Dx = e^Dx/Dx.

I can't seem to get to the correct answer of e^x . I have no problem with this proof for polynomial functions.

Thanks in advance.