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See Also Flashcards What is a Eulerian trail?? A trail that goes along every edge exactly once. Why isn’t a trail that visits every edge multiple times a Eulerian trail?? Because it visits an edge more than once. What is a Eulerian trail that joins up to the beginning called?? A Eulerian cycle. How many edges does entering a vertex and then exiting a vertex “use up” when constructing a Eulerian trail?? 2 Why must all vertices be even for a Eulerian trail to be possible?

See Also Flashcards What is a Hamiltonian cycle?? A cycle that visits all the vertices of a graph. How many times should a Hamiltonian cycle visit a vertex?? Just one, apart from at the end. What must be true about the start and end vertex of a Hamiltonian cycle?? It must be the same. What is the formula for the number of Hamiltonian cycles for a complete graph $K_n$?? $$ \frac{(n - 1)!}{2} $$ Backlinks [[Further Maths - Syllabus]]S [[Further Maths - Graphs]]S Metadata date: 2021-11-04 12:14 tags: - '@?

Flashcards Why is it good to carefully choose the point where you take moments?? Because you can ignore the rotational effect of any forces acting at that point. Why is it good to take moments at $R_A$ or $R_C$ here rather than halfway down the rod?? Because you only get 1 unknown. 2021-11-17 If a rigid body is tilting about a pivot, what can you say about the reaction at any other support?? It is zero.

Flashcards What is a parametric equation?? An equation where $x$ and $y$ are defined in terms of a parameter $t$. How do you work out points for a parametric curve?? Plug in a value for $t$ and see what co-ordinate $(x, y)$ it generates. How can you convert a parametric curve to a Cartesian one?? Rearrange $x$ or $y$ to $t = …$ and then substitute. Backlinks [[Maths - Syllabus]]S Metadata date: 2021-10-05 18:04 tags: - '@?

See Also Flashcards What two points define the Kelvin scale?? Absolute zero Triple point of water What is the triple point of water?? The point at which water is a solid, liquid and gas simultaneously. How can you have a solid, liquid and a gas simultaneously?? By setting an exact pressure and temperature. What is $0K$ in Celsius?? $$ -273.15^\circ $$ What is $0^\circ$ in Kelvin?? $$ 273.15K $$ What is the equation for converting Kelvin $T$ to Celsius $\theta$?

Flashcards What is the time period $T$ of an object in uniform circular motion?? The time taken to complete one rotation. What are the SI units of angular velocity?? $$ \text{rad},s^{-1} $$ How can you conceptualise angular velocity in terms of derivatives?? It’s the rate of change of angle. What is the formula for a radian angle $\theta$ in terms of arc and radius?? $$ \theta = \frac{\text{arc}}{\text{radius}} $$ What is the formula for angluar speed?

Flashcards 2021-07-05 When is a photon emitted from an atom?? When an electron makes a transition. What is the energy of the photon created when an electron drops an energy level?? The difference in energy between the initial state and the new state. What happens when an electron drops an energy level?? A photon is emitted. Why do simple elements have simpler emission spectra?? There are less electron shells and therefore less possible transitions. What type of spectrum is this?

$$(a + b)^12$$ What would you use to expand this?? The binomial theorem. What is the $r$-th term in the binomial expansion of $(a + b)^n$?? $$ \left(\begin{matrix} n \\ r \end{matrix}\right) a^n b^{n - r} $$ $$1 \quad 5 \quad 10 \quad 10 \quad 5 \quad 1$$ What is the next row of Pascal’s triangle?? $$ 1 \quad 6 \quad 15 \quad 20 \quad 15 \quad 6 \quad 1 $$ What does the $n$-th row of Pascal’s triangle start with (ignoring the top)?

See Also [[Maths - Differentiation]]S [[Maths - Chain Rule]]S Flashcards If $y = uv$, what is $\frac{dy}{dx}$?? $$ u\frac{dv}{dx} + v\frac{du}{dx} $$ If $f(x) = g(x)h(x)$, what is $f'(x)$?? $$ g(x)h'(x) + h(x)g'(x) $$ How would you explain the product rule in English?? To find the derivative of two things multiplied together, add the products of the pairs of each function and its opposite’s derivative. This diagram represents $h(x) = f(x)g(x)$.

When is terminal velocity reached?? When the resultant force on a falling object is zero. What’s the formula for percentage difference?? $$ \text{percentage difference} = \frac{\text{actual} - \text{yours}}{\text{actual}} $$ What’s an alternative to the words more/less or goes up/down in Physics?? Increases. What’s an alternative to the phrase “balanced forces”?? Net force or resultant force is zero. What is the centre of gravity?? The point on an object at which the entire weight of the object may be considered to act.