Winter Loving Guy

Trying to find the following derivative of the given function.

y = (4x + 3)^1/2 / 2x

Answer is -2x - 3 / 2x^2 (4x + 3)^-1/2

It's the upper portion of the answer that I can't seem to get right.

f (y) = 3y / 1 - 5y

Answer ends up being 3 / (1 - 5y)^2

It's getting the 3 portion that I don't seem able to get to.

Trying to solve the equation below:

y = (2x - 1)^3

slope of -1/24, x > 0

But I don't even come close to the answer of y - 8 = -1/24 (x - 3/2) or 2x + 48y - 387 = 0

y = x^2 - 2x, it's a tangent line with a slope of 2.

The answer should be y = 2x - 4

Is the solution to simply take the derivative which gives me:

dy/dx = 2x-2

Which I then put in standard y = mx + b form?

Which in turn would give me y = 2(x -2)

Which gives me the y = 2x - 4 answer in my book?

I need to find the center and vertices of the conic section.

4y^2 - x^2 - 4x - 8y - 4 = 0

From there I would group my X and Y terms and move the -4 to the other side.

(4y^2 - 8y) - (x^2 - 4x) = 4

The next part is where I get confused when I take the 4 out of the 4y^2 as a common factor.

4(y^2 - 2y ) - (x^2 - 4x ) = 4

In the next step, it shows me inputting a 1 with my y-terms and a 4 with my x-terms, this is the part that always confuses me. Can anyone explain how I properly get to the 1 and the 4 in those empty spots?

I have a problem for an ellipse, with a vertex of (10, 0) and focus (8, 0), I just need to know what the tangent to x = - 10 part refers to.

Need to find the equation to a concentric circle.

x^2 + y^2 = 6x passes through (4, -3)

The answer is x^2 - 6x + y^2 -1 = 0

I do get the above answer if I first write it out as x^2 + y^2 = 6x + 4 - 3 then move everything to the other side but I do have quite the feeling that's the incorrect way to do it.

Find the Equations of the Ellipses Satisfying the given conditions. The center of each is at the origin.

Vertex (8, 0)

Pass through (2, 3)

The only part I seem to be getting correct so far is the squaring of 8 to 64, as the final answer should be:

X^2/64 + 15y2/144 = 1

or

3x^2 + 20y^2 = 192

Trying to make sense of the problems in my book but there's no real easy to follow examples.

Trying to solve this problem now:

Find the equation of the parabolas satisfying the given conditions. The vertex of each is at the origin.

Passes through (3, 3) and (12, 6).

The answer in the back is y^2= 3x

Has a slope of -3 and passes through the intersection of the lines 5x - y = 6 and x + y = 12

What steps do I take to get to the answer of 3x + y - 18 = 0

This is to all Trance fans out there. My friend is trying to find the title of a Trance song which she believes is one of the more earlier, popular trance songs. All she remembers is one of the lyrics being 'America' and in the video, the song takes place in a raging storm on a see with a very skinny, almost skeletal guy.

Any help would be appreciated as trying to remember the name of the song as well as the name of the band/DJ as this is driving her crazy.