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For part (v), use the gradients of tangents at P & Q and the formula: tan(theta) = |(m<SUB>1 </SUB>-<SUB> </SUB>m<SUB>2</SUB>)/(1 - m<SUB>1</SUB>m<SUB>2</SUB>)| Work through the algebra and you will get tan(theta) = 12/[5sin(2theta)] Keep in mind that b<SUP>2 </SUP>= a<SUP>2</SUP>(1 -...

The cone has radius of base = 24 and height = 30. At any height = h, the water surface will have radius = r. Use similar triangles to write r in terms of h. 24/30 = r/h => r = (4/5)h Substitute into V = (1/3)*pi*r^2*h to obtain the volume V = (16/75)*pi*h^3. Differentiation gives...

dA/dx = 5 - 2e^2x dA/dt = -9.8 From these obtain dx/dt. Substitute x = -0.3.

A(-6,4), B(4,4) and C(0,0) First, let the midpoints of AB, AC, BC respectively be L, M, N. The coordinates of these points are easy to obtain using the midpoint formula. L(-1, 0) M(-3, 2) N(2, 2) Next, find the gradients of sides using the gradient formula. Gradient of AB = 0...

By distance formula, OA^2 = c^2 + c^2 = 2c^2. Therefore, OA = sqrt(2)c.

Hint: Use the locus definition to write PS+PS' as ePM+ePM'.

Precisely. Thank you.

Burwood Girls High School 2006 - 99.95 There was a couple of them. One girl I know personally but I'm not sure if the others got 99.90 or 99.95. However I have heard from teachers and ex-students that the cohort of '06 was very weak overall, which might explain why the school's ranking fell...

If pq=2 then the normals intersect at N[-2a(p + q), a(p^2 + q^2 + 2pq)] Notice how if T = -(p + q), then T^2 = [-(p + q)]^2 = p^2 + q^2 + 2pq N[-2a(p + q), a(p^2 + q^2 + 2pq)] can then be expressed as (2aT, aT^2) and this satisfies the parametric equation of the parabola.

Quite clearly, because p and q are both arbitrary third party parameters, they are perfectly interchangeable and it makes no difference what you use to represent either endpoints of a chord. a) Use two-point formula. b) Substitute (0, -a) into the equation for PQ. c) Use distance formula...

z<SUP>2</SUP> + 2(conjugate of z) + 1 = 0 is not a polynomial because z and conj.z do not represent the same pronumeral. The fundamental theorem of algebra does not apply here. It works out very easily using the substitutions z= x + iy & conj.z = x - iy: (x + iy)^2 + 2x(x - iy) +1 = 0 x^2...

On the brighter side, the same sight fills me with motivation. Try that. Thank you, I do appreciate the support. The fair number of people above who are ranked 1st in every subject they do are truly AMAZING. I still have some way to go.

Aside from the fact that I need to tighten up my Adv English, MX1&2 ranks. I shall hope for the best now that I've shed my last back-up unit. And I bear no doubt that you will get a similar, if not greater, UAI. I'm rather glad we're not competing for the same course.

Advanced English Mark: 23/25, 14/15 Cumulative Rank: 4/91 Extension-1 English Mark: 10/10 Cumulative Rank: 1/27 (I quit though.) Maths Mark: 48/48 Rank: 1/74 Cumulative Rank: 1/74 (Strangely we were ranked with the 2U-ers. Too bad this counts for nothing.) Extension-1 Maths...

The German owns the fish, although I'm not entirely confident. This is the order of things as I worked them out: 1st house: yellow, Norwegian, cats, water, Dunhill 2nd house: blue, Dane, horses, tea, Blend 3rd house: red, Brit, birds, milk, Pall Mall 4th house: green, German, fish, coffee...

Take a look in www.uac.edu.au

I assume it's the silver oxide button cell you're talking about. One thing is that silver is a heavy metal and bioaccumulation can be harmful to the environment. Really, read through textbooks & study guides.

1) I think this will be taught in various ways by different teachers. In my chemistry class we have to do 3+ titrations so that we produce at least 2 consistent values. Our teachers says if you get 2 equal values then you use this value; if all 3 values are different but are within +-0.1 of each...

I finished Volumes on Monday and I've started Polynomials. Is anyone else planning to cover some Ext-2 topics on their own in this holiday?

Shouldn't take you long to finish 2U/Ext-1 app of calc in the physiscal world. I think that topic also includes rates of change and exp growth/decay so there's not very much on motion to begin with. If you try not to simulataneously have an X-files marathon like I shamefully had, it'll take you...