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Q1 Find the coefficient of x^2 in the expansion of ( x + 1/x)^3 (x - 1/x)^5. First we write (x - 1/x)^5 = (x - 1/x)^3. (x - 1/x)^2 and then substitute it in the relation above and use the property a^n.b^n = (ab)^n and (a + b).(a - b) = a^2 – b^2<O:p</O:p we can rewrite: <O:p (x^2 -...

First of all, you seem very confused at this stage. My suggestion is to not take any advice before clarifying yourself first, as no one else knows better then you what you can /can’t do. HSC is a matter of being effective/ efficient (get the best results with the least amount of effort) and make...

That's right, you cannot sit both exams as they are always held in the same day at the same time, which means you can choose either 2 unit or extension 2.

As you said, the first digit must be 7, so there are 7 places left, for each of them having 10 possibilities (0-9). So the total number of phone numbers is : 1X10^7 (the numbers can be formed in 10^7 different ways)

Let’s consider 2 complex numbers z1=x1+iy1 and z2=x2+iy2. The numbers can be represented geometrically on the complex plane (Argand diagram) as 2 points A(x1,y1) and B(x2,y2). They can also be represented as 2 vectors, both starting from origin O(0,0) towards A(x1,y1) and B(x2,y2)...

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Have fun!:wave:

Have fun!:wave:

Happy studying!:wave:

I’d say that the question is asking the sum of: 1 + 2 + 4 + 8 + … + 1024, which are powers of 2 from 1 = 2<SUP>0</SUP> to 1024 = 2<SUP>10</SUP>. So we have a geometric series with a =1, r =2 and n = 11 (from 0 to 10 there are 11 terms). S<SUB>11</SUB>= 1(2<SUP>11</SUP> – 1)/(2-1)=2<SUP>11</SUP>...

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T = -40 + Ae^kt When t = 0, T = 24!!!, not A 24 = -40 + Ae^0 So A = 64 T = -40 + 64e^kt When t = 5, T = 19, so k = ln(59/64)/5, which is negative. Find t=?, for T =0. t = 5ln(5/8)/ln(59/64) t = 28.9 sec. Good Luck!!!!!!!!:wave:

We can use the formula for the perpendicular distance from a point to a line. However, in our case it’s easier to notice that the point P has the coordinates x and y (given) and the line is x-axis (y = 0), so the distance is the length of the segment from P to the foot of the perpendicular on...

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Hope it helps.:hammer: Good luck!!!