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Well if the costs (solutions for x1, x2, x3, x4 from my post) came out to be very large (say 1,000,000 or something), that'd be fishy, because clearly a trip wouldn't cost that much. Basically, if the costs came out to be anything "unreasonable", something must be up.

To use LaTeX on this site, we enclose LaTeX code in tex tags. There's a Short Guide to LaTeX on this site here: http://community.boredofstudies.org/14/mathematics-extension-2/234259/short-guide-latex.html e.g. To get x^2, write [ tex] x^2 [ /tex] (without the spaces I put in the tex tags; I put...

$\noindent Let $x_i$ be the cost for route $i$ ($i=1,2,3,4$). Let $b_A,b_B,b_C,b_D$ be the amounts claimed in total by Executive $A,B,C,D$ respectively. Then we must have the following matrix equation: $A\vec{x} = \vec{b}$, where $A$ is the matrix (table) given to us, $\vec{x} =...

$\noindent If you want the magnitude and direction of the net force vector in part 2), here's how to find them. Recall that the net force was $\vec{F}_\text{net}=\left(250-75\sqrt{2},200 - 75 \sqrt{2}\right)$. Hence $\left \| \vec{F}_\text{net} \right \| = \sqrt{\left(250-75\sqrt{2}\right)^2...

$\noindent 1) Say the river has its banks parallel to the $x$-axis in the Cartesian plane. Say the current is $1$ km/h to the right, so we can draw the current vector $\vec{c}$ as a vector from the origin pointing right 1 unit. Say we want to go from the lower bank to the top. Our velocity...

Voltage. See this page (especially the 'Electromotive Force (EMF)' section): http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elevol.html .

Re: MATH1131 help thread $\noindent We have $x \geq \frac{6}{x-1}$ (note $x\neq 1$, since then we have a zero denominator). We'll do it in cases.$ $\underline{Case 1. $x >1 $}$ $\noindent Here, $x-1>0$, so when we multiply through the inequation by $x-1$, we don't change the sign. On...

Re: HSC 2016 2U Marathon $\noindent It's $y=1$ or $x=0$, excluding the point $(0,0)$ since $0^0$ is undefined. So it's a pair of lines excluding one point.$

Those are examples of monomials: https://www.mathsisfun.com/definitions/monomial.html . They are also special cases of power functions where the index is a positive integer: https://en.wikipedia.org/wiki/Power_function .

This would require the assumption that the initial velocity is 0 (i.e. it starts at rest), which is not given to us. Like imagine releasing a pendulum (this is approximately a simple harmonic oscillator for small angles of amplitude). Its angular frequency is inherent (based on the length of...

This question is incomplete. We are only given one initial condition, but for a second order differential equation, we'd need two initial conditions to completely determine the behaviour of the system. So we can't determine the maximum speed. If they'd told us something like the particle was...

To deal with the -1, use the triangle inequality as shown by parad0xica.

How do we justify dropping the -1?

Re: HSC 2016 4U Marathon I believe you can obtain an arbitrarily large expected profit by choosing your subintervals to be arbitrarily small and at the endpoints of the whole interval, e.g. choose two intervals like this: [1, 1 – L/2] and [-1, -1 + L/2], and make L arbitrarily small (the total...

"Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces." (From Wikipedia: https://en.wikipedia.org/wiki/Linear_algebra)

1) The method is described here in the 'vector formulation' section: https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line#A_vector_projection_proof 2) The method for finding the distance between two skew lines (non-parallel yet non-intersecting lines, which can exist only in...

Oh, yeah the HSC maths courses (2U and up) are mostly calculus-based. Linear algebra got removed several decades ago I believe.

I know what calculus meant, I meant what did you mean by the 'everything in maths' part.

Re: MATH1131 help thread It's the interior and edges of the triangle with vertices: (0,0), (2,0), (2,4).

$\noindent In fact, Question 2 is related to the Fibonacci sequence (not surprising, as the quadratic equation is the defining equation for the Golden Ratio $\varphi$, which crops up in many things related to the Fibonacci numbers, among other things). The Fibonacci numbers may be defined as...