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Hint: find the limiting reagent.

Here is another way to do Q21 Factorise 3 and complete the square, 3x^2 - x + 7 = 3\left( x^2 - \frac{x}{3} + \frac{7}{3} \right) = 3\left( \left(x - \frac{1}{6} \right )^2 + \frac{1}{6^2}+ \frac{7}{3} \right ) The result is clearly positive for all values of x

Here:

Yes. Draw a diagram. "Magnitude of displacement" is just the distance between starting point and end point. In this case, it's √2 = 1.4142... ≈ 1.4.

Portal 1/2 > Challenger

(Another method) The ball being pulled down 2cm from the origin implies that v = 0 at x = 2 or v(2) = 0. So we need an equation relating v and x. Remember that a = -n^2 x , which means n= 16. By chain rule, a = \frac{dv}{dt} = \frac{dv}{dx} \cdot \frac{dx}{dt} = \frac{dv}{dx} \cdot v...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I'm just looking at the possible ways you can place the Es (or combinations) such that the conditions are satisfied. The placement of the rest of the letters can be ignored since it's all the same for each part of the question

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Did all for fun... but still a bit rusty so it most likely has at least one error ____ We are only concerned on placement of Es so the sample space is \binom{13}{3}. a) Group 3 Es as a blob. There are 11 ways you can place...

x = 0 doesn't work. You are missing something in your solution (-1<x<15/2). Apply what InteGrand said (post #922) and you will get the answer.

Another method is to complete the square: \begin{align*}x(x - 1) &= x^2 - x \\ &= x^2 - 2x + x\\ &= (x-1)^2 -1 + x \\&= (x-1)^2 + (x-1)\end{align*}

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread @davidgoes4wce: Out of curiosity, what font is used for the first row of the table and "Total combinations"?

Re: HSC 2016 3U Marathon Here is a hint. Highlight to see. Also in LaTeX code to try to prevent immediate comprehension in-case you accidentally highlighted or ctrl+A ___ \frac{a^{k+1}+b^{k+1}}{2} \geq \frac{a^kb + b^ka}{2} = \boxed{?}\times \left( \frac{a^k + b^k}{2} \right ) + \boxed{?}...

Hey guys, my name is Patrick and I completed the HSC in 2013 achieving a band 6 in 2U and E4s for both 3U and 4U. Reiterating: I'm a third year Advanced Maths/Comp Sci student studying at UNSW and I offer private one-on-one tutoring for 2U and 3U. Aim To give you more confidence when doing...

Re: HSC 2016 3U Marathon Yeah! I made a little typo on the denominator

Re: HSC 2016 3U Marathon Assuming a is A and b is B, could there possibly be a typo in the question? Suppose a = 0.1, b = 0.2 and n = 3. Then \left(\frac{a+b}{2} \right )^2 = \left(\frac{0.1+0.2}{2} \right )^2= 0.0225 \frac{a^n+b^n}{2} = \frac{0.1^3 + 0.2^2}{2} = 0.0205 Therefore...

How long has it been since you did the entrance exam? The mark does not matter if you want to get accepted, it's the last question that matters ^_^

Do you know a relationship between a polynomial's roots and it's coefficients?

High chance this person is a female but this is judging from a small population and one person's observation. I noticed that females are more likely to add a "bubbly"-style to their handwriting than males. However, the curvature of the letter "y" and the terminating point of the tail is...

Can you post your working?

According to wolframalpha, the answer provided is right