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Hey your really good! I figured this out after sitting down and playing around a bit and writing the DE again. :)

If water was leaking from an inverted conical tank at a rate of 10 000 cm³/min and at the same time water form another source is entering the tank at a constant rate Q. The tank is 6m high and the...

Yep this is the diagram I was describing I also worked out the gradient function as y=3x+6 but didn't know how to take it from there to relate it to what I need, but the formula given below shows a...

Thanks for the reminder of this formula, I would have never thought of using it, I'm not naturally talented with numbers so many concepts and formulas are forgotten if not used, a few months after...

I can't seem to get my head around this question, if I had a point P(x,y) that moves along the line y=3x and I have another point Q which is stationary at (2,0), I need to write an expression between...

Thanks I tried to group the 2c+2b+4a together and also tried working this out simultaneously, but from how u worked this out makes so much more sense. And yep subbing back into the DE works :)

If y=a+bx+cx^2 is a solution of d²y/dx² +2(dy/dx)+4y=4x², I have tried to find the values of a,b and c by taking the derivative and second derivative of the function the subbing these into the...

Hey thanks I get confused about which form to express it in to work out the solution, I had tried to put it in polar exponential form and didn't think on expanding etc.

No, apparently the answer is .5(1-i(sinbeta/1+cosbeta).

If you haven't noticed it's the end of semester break, so this isn't for homework, just asking these questions to tie up loose ends.

Can someone show the workings to finding the roots of:

(Z+i)^5 - (Z-i)^5=0

Apparently it can be done using complex exponentials and roots of unity (whatever that means), anyway the answer is...

This isn't the answer given in my book. The answer given is
plus or minus one plus or minus i root three. Thanks for trying but, spinning me out too :)

Can someone show me how to find the roots of:
(Z^4)+(Z^3)+(Z^2)+Z+1

Please show how you worked this out. Thanks

Need to find the roots of :

1) ( z^4)+(4z^2)+16=0

2) (z+i)^5-(z-i)^5=0

thanks :)

How would I simplify this:

((1-i)/(√3-i))^7

Thanks again ;p

Express in cartesian form a+ib, with a,b as real numbers:

1/(1+cosβ+isinβ)

Thanks ;p

Can anyone help me with finding the solutions to:

(z^8)-256=0

I can find z= 2, -2, 2i, -2i but don't know how to find the other 4 solutions, apparently I can let z^2=(a+ib)^2 and solve for a...

A eukaryotic auxotroph would be i.e. plants as they are multicellular and make their own nutrients via photosynthesis etc. Sorry this may have come to u too late, just saw this now.

Can someone explain how this is done:

Let L1 be the line through the points P(4, -1,1) and Q(1,0,-3) and

L2: (x-3)/4=(y+2)/-2=(z+5)/3

1. Find the vector equations of the lines L1 and L2.
...

There are multiple treatments available but none too promising. Surgery can remove the affected tissue (pleurectomy/decortication etc) with a combination of chemotherapy and radiation treatment. At...

Yes, Mesothelioma is a cancer of the mesothelial tissue (membrane lining the heart, lungs etc) and is associated exposure to asbestos earlier in life. An accumulation of mutations in the cells over...

Yep but if I use double angle formulas to expand to simplify I will end up separating the variables inside and it can' t be simplified :{

Hi again, was wondering how to solve this question:

let v vector be from A(2, 0, -1) to B(1, 2, -3) find 2 vectors parallel to v vector.

I found that v=B-A=(-1,2,-2) but don't know how to find...

Am I mistaken but a question such as expand and simplify:

tan((pi/2)-y) and cot((3pi/2)+x) can't be done as tan of pi/2 and 3pi/2 are undefined? I got these questions out of a maths book with no...

Hi, was wondering how I would display or plot vectors with I, j and k components. Can do it when there is only I and j (2 components-just x and y axis). I know there is a x,y and z plane but don't...

Was wondering how you worked out that they aren't dying out.

I see... one of those tricky questions eh? Are you sure? Because in 3 hours there is 9000 and in one hour of poison 4500 are knocked out, so in two hours shouldn't that wipe out 9000, taking in...

If I am culturing an organism and it is growing at a rate proportional to the number, N, of organism present so that:

dN/dt= kN

t is the time elapsed in hours and k is a constant, initially the...

wouldn't know were to begin with shells, I thought that may be the case that you probably forgot to include the absolute symbol. But I don't know the technique you used to expand ((x-2)^2)^2 I know...

Yes, thanks, that's probably the problem, there should be a better explanation than "you must spread the reputaion".

Your getting carried away is extremely welcomed!! Your graph is crazy.. lol!! But when I integrated I ended up with a -ve no so I went back and expanded g(x), I think you left out the -ve, after...

How would I find the volume enclosed by these two curves if I were to rotate it about the x-axis?

curves: y=x and y=(x^2)-4x+4

I know the curves intersect at x=1 and 4, I think that the area...

You're the best!! Spent ages trying to work this one out. I don't know how to rate the answer, so please excuse me if I don't somehow rate it.:D

How do you solve an initial value problem:

dy/dx= xe^(y-x^2) and y(0) = 0

Can someone tell me how to evaluate the integral:

∫tan(2x)sec³(2x)dx

I don't know what to do when sec is cubed and which substitution to make, or if there even is a substitution, if I express...

Hi, I've done what you've suggested and got:

x-2(x-4)log(√x-2)+C is this correct? I don't know if I applied it correctly, or do I apply the 2(u+2) to the right hand side as well as that is also?

Thanks you're a legend! ;p

Does this mean this mean that I find the integral of e^(tan(X)), then is the answer e^(tan(x))/tan(x) +C ?

Hi there, with this question you should remember the trig identity tanθ=sinθ/cosθ and cos squaredθ plus sin squaredθ=1

so you have: to prove that Left Hand Side=Right hand side

(LHS)...

Remember that tanθ=sinθ/cosθ

so you have tanθ/sinθ this is the same as (sinθ/cosθ)*(1/sinθ)

(it is easier to see if you wrote this out on paper)

this cancels the sinθ and you end up with...

How would one tackle such a problem? Antiderivative of:

((√x)-4)÷((√x)-2)

Can anyone help me in finding the antiderivative of:

sec²(x)e^(tan(x))

Antidifferentiation is so confusing!!

This is some situation your in, I have a younger, skinnier sister also. You've got to step back and relax, has your sister got a boyfriend? If she's as hot as you think she probably has and the...

A section of blood vessel has a flow-rate F in cubic millimetres per
Minute proportional to the fourth power of its radius, R. The blood vessel can be
Considered perfectly cylindrical and is...

Can anyone tell me how to find the derivative of:

xy = tan(xy) and of

x² =arctan(y)/(1 + y²)

Very much appreciated, as soon as possible please, I really have no clue when there is both x and...

Thank you :)

Use implicite differentiation to get the derivative of the function, also re-arrange the original equation to make y the subject and sub that in for y in the differentiated equation. Now that you...

Inflate a spherical balloon by blowing 1000cm³ of air into it every 5 secs:

a) What is the rate of change of the volume of the balloon (in cm³/sec) at the moment when the radius of the balloon is...