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Hi. My name is Nathan and I am offering 3/4 maths unit and economics tutoring to anyone in the inner west and city areas. Relevant Credentials: ATAR: 99.55 Extension 1 - 98 Extension 2 - 97 Economics - 96 Rate: $35/hr (2 hr lesson – if required to travel) $25/hr (2 hr lesson – if at my...

Can someone help me out with these questions. 1)Use z^n + z^-n = 2cosn@ to solve 2z^4 + 3z^3 + 5z^2 + 3z +2 =0 2) Solve (z-1)^4 = 16(z+1)4

Can somebody help me with this one. \int \frac{dx}{(4+x^2)^\frac{3}{2}} using x=2tan\theta

Show: 2sin^{-1}\frac{3}{5}=sin^{-1}\frac{24}{25} and sin^{-1}\frac{3}{5}+tan^{-1}\frac{7}{24}=cos^{-1}\frac{3}{5} I have no idea where to start in both of them except for drawing triangles.

The Cmbridge book does not explain properly. Can someone guide me through the steps. cos3\Theta=4cos^3\Theta -3cos\Theta Solve for 8x^3-6x-1=0

4x^3+12x^2-15x+4 You are given that the polynomial has a double root. Find all the roots using the idea of multiplicity of roots.

Hi. I got a question here is can't seem to solve. Tangents at P(x_1,y_1) and Q(x_2,y_2) from the curve x^2=4ay intersect at M(\frac{2a(y_2-y_1)}{x_2-x_1},\frac{x_1y_2-x_2y_1}{x_2-x_1}) Using x_1^2=4ay_1 \and\ x_2^2=4ay_2, show M is (\frac{x_1+x_2}{2},\frac{x_1x_2}{4a}) I've got the...

x=3+rcox@ and y=-2+rsin@ If @ is constant and r is variable Source: Cambridge Maths 3 Unit Year 11

Hi. I got 2 questions which I'm stuck on. 1) The tangent and normal at any point P on an ellipse meet the major axis at T and G respectively. If PN is the ordinate of P and C the centre, prove that CT.NG=b^2 2) P is a point on the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 with centre O. A...

x=t-\frac{4}{t} y=\frac{t^2}{2}+\frac{8}{t^2} How can I solve that to get to x^2=2(y-4)

Find the equation of the tangent at the point (3,-4) to the circle x^2+y^2=25. I got the answer to be 3x-4y=25 What are the equations of the two tangets parallel to the y-axis? I got x=5 and x=-5 Show that the first tanget intersects these tangets in points which subtend a right angle at...

How do you draw arg(z-a)=arg(ia) At first I thought it was the 2 lines extendng from points a and ia, but then I realised arg(ia) isn't the same as arg(z-ia)

If A,B represent z1 and z2 OAB is equilateral, prove (z_1)^2+(z_2)^2=z_1z_2 What am I doing wrong? Or do I have to do soething with multiplying by Cis pi/3 LHS= |(z_1)^2|+|(z_2)^2| |z_1|^2+|z_2|^2 Let common modulus be z |z|^2+|z|^2 2|z|^2 RHS= |z_1z_2| |z_1||z_2|...

Show that the equation x^2 +kx +1 = 0 has complex roots with unit modulus provided -2<k<2

Can somebody teach me some general tips in reading the graph of the derivative.

Hi. I've finally figured out how to graph composite functions and now I'm up to implic differentiation and graphing it. The textbook has a small explanation but it isn't clear enough. Can anyone explain to me. Hopefull Jetblack you can help me out again. Eg x^0.5 + y^0.5 = a^0.5

Hi. I've got a question here. You don't have to answer it, but it would certainly save me some time. Is it possible to get answers for all these questions. A lifeboat is dropped from a plane at 100m/s from a height of 1000km (just rounding the numbers off) a) initial velocity b) initial...

Hi. I'm not sure how to do integration by substitution when one the substitution they give us is a square. Eg. u^2=x+2 Find\int \frac{x-2}{(\sqrt(x+2)}

Hi. I'm not sure how to answer questions involving midpoints where multiple parameters are used. Eg. Locus of the midpoint of P and Q on x^2 = 4ay where the x-coordinate differ by 2a

Hi. I'm not really sure about the theory behind graphing functions that look like f(x) = f abs(x) eg. f(x) = ln abs(x) Can someone please clarify.