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Hi everyone, I've got a few First Year Commerce textbooks up for sale. The books are listed below: ECON1101 - Principles of Microeconomics 2E (very good condition with some useful highlighting) $65 (RRP: $112.46) ACCT1501 - Financial Accounting An Integrated Approach 4E (very good...

Use the fact that f(x)=(ax-b)^2+(cx-d)^2\geq 0 to prove |ab+cd|\leq \sqrt{a^2+c^2}\sqrt{b^2+d^2} (a,b,c,d real) It's obvious if you just use 2abcd\leq a^2d^2+b^2c^2 to prove \sqrt{(ab+cd)^2}\leq \sqrt{(a^2+c^2)(b^2+d^2)} but how would you do the question using f(x) ?

The hyperbola x^2/a^2 - y^2/b^2 =1 has one focus S on the positive x axis. The circle with centre S and radius b cuts the hyperbola at points R and T. If b=a, show that RT is the diameter of the circle. when i attempted this question i got: (x-ae)^2 + y^2 = a^2 x^2 - y^2 = a^2 Solving...

A solid is formed about the ellipse x^2/25 + y^2/9 =1 in such a way that each plane section of the solid perpendicular to the x-axis is an ellipse whose foci are on the given ellipse. The major and minor axes of each section are proportional to those of the given ellipse. Determine the volume of...

Hey, are the questions from the Coroneos supplement book any good for topics like conics and volumes?

What are some dependent and independent variables for the heat of combustion experiment and the titrations experiment? Thanks

A railway line around a circular arc of radius 800m is banked by raising the outer rail h metres above the inner rail, where the distance between the rails is 1.5 metres. When the train travels around the curve at 10m/s, the lateral thrust on the inner rail is equal to the lateral thrust on the...

Is there a way to prove this without induction? 1^2 + 2^2 + 3^2 +...+ n^2 = n(n+1)(2n+1)/6

A particle is moving vertically downward in a medium which exerts a resistance to the motion whithc is proportional to the speed of the particle. The particle is released from rest at O and at time t its position is at a distance x below O and its speed is v. isnt the equation of motion...

4 boys and 4 girls sit around 2 concentic circles such that there are 4 in each circle. In how many ways can they be seated if boys and girls sit around different circles. Can someone tell me whats wrong with this: If boys in inner circle, 3! ways to seat boys, 3! ways to seat girls, but...

x=\int_{0}^{t}vdt Does this apply for any function v? Also, what is the proof/explanation to this? Thanks

If w=cis(2pi/8)=cis(pi/4). Prove (1-w)(1-w^2)(1-w^3)...(1-w^7)=8

Can you assume the volume of a cylinder is (pi)(r^2)(h) when doing questions?

True or false: \int_{0}^{1}\frac{dt}{1+t^n}\leq \int_{0}^{1}\frac{dt}{1+t^{n+1}} for n=1,2,3,... It's false cause they cant be equal right?

\int_{e}^{e^4}\frac{dx}{x\ln x} for the above question you could easily use the substitution x=lnx but if we were to use parts, we get: 2\int_{e}^{e^4}\frac{dx}{x\ln x}=[\frac{\ln x}{\ln x}]^{e^4}_{e} by letting u=\frac{1}{\ln x} and v=\ln xdx Whats with that? How can you have 1...

The Fibanacci sequence is defined by t_{n+2}=t_{n+1}+t_{n}. Find the limit of \frac{t_{n+1}}{t_{n}} as n goes to infinite.

Just wondering if there is an alternative method to t method to solve int[1/(1+sinx)]. I know t method doesnt take long but just wondering if there are alternatives. Any replies would be appreciated

need help with 2 questions: 1. By considering 1+\binom{n}{1}x+\binom{n}{2}x^2+...+\binom{n}{n}x^n=(1+x)^n, show that 1-\frac{1}{2}\binom{n}{1}+\frac{1}{3}\binom{n}{2}-...+(-1)^n\frac{1}{n+1}\binom{n}{n}=\frac{1}{n+1} 2. Prove that...

I was doing this question and i got to a point where i found that (1-2k)>0.5. I need to find an inequality with (1-2k)/k^2 in it given 0<k<0.25. Can i just go from the first step to [(1-2k)/k^2]>8 or do i need some sort of explanation. If so, what should i write?

f(t) = 4-4t/3 for t is between or equal to 0 and 6 = t -10 for t is between or equal to 6 and 12 F(x) = \int_{0}^{x}f(t)\,dt Calculate F(12) (The answer is -6)