Zikro

Keep in mind the idea is to start with the rectangular equation format (cartesian?) and then convert that to polar.

It's 3 parts, an ellipse, a parabola, and a hyperbola. I'm starting with the ellipse and haven't been able to figure it out.

Ellipse problem: "Find a polar equation for an ellipse that has foci (0, +-3) and vertices (0,+-5)."

As far as I'm aware we're using a horizontal ellipse equation so (x^2/b^2) + (y^2/a^2) = 1. Given the provided info, a = 5 and c = 3. Using given relationship for ellipses: c = sqrt(a^2 - b^2) I found b = 4.

This gives the equation (x^2/4^2) + (y^2/5^2) = 1. I don't know where to go from here in the process of converting this equation to polar. I know that x=rcos(0) and y=rsin(0) and r^2 = x^2 + y^2. Note that 0 is place for theta. Substituting for x and y gives me the equation...

(r^2cos^2(0)/16) + (r^2sin^2(0)/25) = 1. My algebra is spotty in this scenario so I'm not sure what to do with the 16 and 25 (if I multiply by 16 to get rid of it what happens to the 25? does it become 9?) and I don't really have any idea of what the end result should look like either...

I'm mainly looking for help with this problem because I think it'll guide me in solving the parabola and hyperbola but here are the specifics for those as well in case anyone is feeling generous or something.

Parabola Problem: "find a polar equation for a parabola that has its vertex at the origin and the Directrix y=-10"

Hyperbola Problem: "find a polar equation for a hyperbola that has vertices (0,+-6) and asymptotes y=+-(1/3)x

That's supposed to be a theta (as in angle) not a zero or letter.

"Start with the equation sin(0) = cos(0). Use the unit circle interpretation of the circular functions to find the solutions of this equation; describe your reasoning."

Help please. Thanks :]

I'm given 6 equations and asked for the domain, the x and y intercepts and to sketch a graph to indicate asymptotes along with finding equations for the asymptotes. Help with a couple examples? I'll post all 6 equations but I'm not really expecting anyone to show them all. If you could explain the process in one or two, that would be great.

a) f(x) = (2x)/(x-1)

b) g(x) = (3x+2)/(2x-5)

c) h(x) = (x+1)/(x-2)

d) j(x) = (4x-12)/(x+8)

e) k(x) = (8x+16)/(5x-0.5)

f) m(x) = (9x+24)/(35x-100)

I'm given 6 equations and asked for the domain, the x and y intercepts and to sketch a graph to indicate asymptotes along with finding equations for the asymptotes. Help with a couple examples? I'll post all 6 equations but I'm not really expecting anyone to show them all. If you could explain the process in one or two, that would be great.

a) f(x) = (2x)/(x-1)

b) g(x) = (3x+2)/(2x-5)

c) h(x) = (x+1)/(x-2)

d) j(x) = (4x-12)/(x+8)

e) k(x) = (8x+16)/(5x-0.5)

f) m(x) = (9x+24)/(35x-100)

I'm given a unit hyperbola (x^2 - y^2 = 1). For any value a, show that the point (x,y) = [cosh(a), sinh(a)] is on the unit hyperbola. There is a hint provided which is the question title: "Verify that [cosh(x)^2] - [sinh(x)^2] = 1, for all x."

Show that, for every value of a, the function

f(x) = a + (1/(x − a))

is its own inverse.

???

I don't understand this concept and my math textbook appears to not even teach the concept at all.

Write each of the following functions as a composition of two simpler functions:

(a) y = (x − 11)^5

(b) y = 3sqrt(1 + x^2)

(c) y = 2(x − 3)^5 − 5(x − 3)^2 + 0.5(x − 3) + 11

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

(e) y = sqrt(sqrt(x) + 1)

(f) y = 2 - sqrt(5 - (3x - 1)^2)

Sylvia has an apple orchard. One season, her 100 trees yielded 140 apples per tree. She wants to increase her production by adding more trees to the orchard. However, she knows that for every 10 additional trees she plants, she will lose 4 apples per tree (i.e., the yield per tree will decrease by 4 apples). How many trees should she have in the orchard to maximize her production of apples?

I've tried all sorts of approaches but can't figure it out... I know the answer is 225 but I do not know how to reach it. I assumed I need 3 equations but that gives me 3 unknowns and I tried the elimination method unsuccessfully. I think I'm making this problem a lot harder than it should be... Any help is much appreciated!!

I cross multiplied and added like terms and came out with:

[(x^2 - 7x) / (x^2 - 4x - 21)] + [(5x + 15) / (x^2 - 4x - 21)] = [30 / (x^2 - 4x - 21)]

So now they all had a common denominator and then got:

(x^2 - 2x - 15) / (x^2 - 4x - 21)

Now I don't know how to simplify it any further from here. Help please. The back of the textbook says the answer is x = 5. How do I arrive to that point?

Additionally (would be nice if you could help):

(b) sqrt(5x - 4) = (x / 2) + 2

(c) sqrt(x) + sqrt(x - 20) = 10

(d) sqrt(2t - 1) + sqrt(3t + 3) = 5

I haven't gotten to the remaining 3 yet so I couldnt post my work on it but I'll get cracking on that currently.

Just for laughs, I get a kick out of those sort of things.

Just looking for some laughs.

Full Question: The line L is the tangent to the curve of f at (3,12). Find the equation of L in the form y = ax + b.

The original function given is f(x) = (1/3)x^3 + 2x^2 - 5x.

I tried to find the derivative by 'completing the squares' (which I dont fully understand) so it may be wrong. Either way, here is what I got.... it may be useful?

y = (1/3)x * (x+3)^2 - 7x

Thanks for help :]

I need a basic equation (nothing too long or fancy but if you must then go ahead) that has holes on the graph. This is for use with integrands (area under the curve). Thank you.

FYI, Geico is the auto insurance company with the Gecko. There is a song that ends the commercials and I wisht o know what it is. Thank you.

Explain how to solve the following indefinite integral:

x^3(10-x^4)^7 dx

Steps and explanations would be appreciated.

Also, is an indefinite integral an antiderivate... aka are they the same thing?

It just began this morning when I woke up. Gonna be honest, I'm scared -.- Never had this before. It hurts when I move my head in certain positions, yawn, swallow, or burp.

In my Bios it says hard drive capacity at 250GB so the motherboard recognizes the hard drive but Windows only says it has 127GB total space, which is effectively half of the actual hard drive size. How to fix this problem?

I connected the HD with Sata cables, not IDE.

I just got a new computer built and it turns out my new computer is lacking a female RGB in the back that my old one had. It only has the serial 1 COM port and I guess I have to use that to connect to my monitor (which is my tv). I used to use a female/female RGB cable (guess thats the same thing as SVGA?) Help please.

Here are images to help explain...

This is the connector my PC/motherboard has:

http://www.cpusolutions.com/mm8004744CPU/Images/IO...

This is what my TV has for its port:

http://upload.wikimedia.org/wikipedia/commons/9/92...

I have to connect them somehow :/

Personally I believe this is hilarious and I have to share this with the world. It's a narrarated break-up letter so enjoy!

http://youmakemetouchyourhandsforstupidreasons.ytm...

Just trying to figure this out for personal research. From what I recall, it is a world in which the rich seperate themselves from the poor in a secluded area. I'm not sure if that is correct and that is the reason I'm here asking for a definition. Please help. Thanks.