@?school

See Also [[Physics - Internal Resistance]]S [[Physics - Voltage and Potential Difference]]S Flashcards If the resistance of $R_1$ is twice that of $R_2$, how much more of the total potential difference does $R_1$ get?? Twice as much. What is the potential divider equation?? $$ V_{\text{out}} = V_{\text{in}} \times \frac{R_1}{R_1 + R_2} $$ Backlinks [[Physics - Syllabus]]S Metadata date: 2021-05-05 15:53 tags: - '@?physics' - '@?

See Also [[Further Maths - Mean Value of a Function]]S [[Further Maths - Improper Integrals]]S [[Further Maths - Hyperbolic Functions]]S Flashcards $$\frac{d}{dx}(\sin^{-1}(x))$$ What is this equal to?? $$ \frac{1}{\sqrt{1 - x^2}} $$ $$\frac{d}{dx}(\cos^{-1}(x))$$ What is this equal to?? $$ -\frac{1}{\sqrt{1 - x^2}} $$ $$\frac{d}{dx}(\tan^{-1}(x))$$ What is this equal to?? $$ \frac{1}{1 + x^2} $$ $$\int \frac{1}{\sqrt{1-x^2}} dx$$ What is this equal to?? $$ \sin^{-1}(x) + c $$

See Also [[Computing - Turing Machines]]S Flashcards What is an insoluble problem?? A problem that is impossible to solve. What are the time complexities for a tractable problem?? Polynomial time, e.g. $O(n^2)$ or $O(n^3)$ What is an intractable problem?? A problem where the computational demands grow so quickly that it’s impossible to solve non-theoretically. What sort of time complexities does an intractable problem have?? Exponential. Backlinks [[Computing - Syllabus]]S Metadata date: 2021-04-28 10:20 tags: - '@?

See Also Flashcards What does Dijkstra’s algorithm find?? The shortest path from every node to a goal node. What are the three columns of the table that get filled in for Dijkstra’s algorithm?? Vertex, shortest distance, previous vertex What is shortest distance to the goal node from the goal node when running Dijkstra’s algorithm?? $$ 0 $$ What is the shortest distance to the goal node from any node but the goal node at the start of Dijkstra’s algorithm?

See Also [[Maths - Integration]]S [[Maths - Integration by Substitution]]S Flashcards What two things mean an integral is improper?? One or both of its limits are infinite It is undefined anywhere in $[a, b]$. What do you call an improper integral that exists (has a defined value)?? Convergent. What do you call an improper integral that does not exist?? Divergent. $$\int^\inft_0 e^{-x} dx$$ What would you write instead to see if it has a defined value?

See Also [[Maths - Integration]]S [[Maths - Integration by Substitution]]S Flashcards What do you divide the definite integral between $[a,b]$ in order to find the mean value?? $$ b - a $$ Backlinks [[Further Maths - Integrating and Differentiating Inverse Trig Functions]]S [[Further Maths - Syllabus]]S Metadata date: 2021-04-27 16:20 tags: - '@?further-maths' - '@?school' - '@?public' - '@?methods-in-calculus' title: Further Maths - Mean Value of a Function

See Also [[Physics - Resistance and Ohm's Law]]S [[Physics - Voltage and Potential Difference]]S Flashcards If $E$ is the E.M.F. of a battery and $V$ is the terminal voltage, what is the formula for “lost volts”?? $$ Ir = E - IR $$ Why are there “lost volts” in a battery?? Because the battery has some internal resistance. Why do the lights on old-fashioned cars blink out when you start the engine?

See Also [[Computing - Recursion]]S Flashcards What are the three rules of recursion?? Base condition The function calls itself Finite amount of runs What is the main disadvantage of recursion?? It uses a lot of memory on the stack. Metadata date: 2021-04-19 16:07 tags: - '@?computing' - '@?school' - '@?public' title: Computing - Recursion

Flashcards What is a loading and unloading curve?? A graph that shows how extension varies with force as a material is being stretched and released. Why is there a difference between the loading and unloading curves for an elastic band?? More work is done stretching (loading) the elastic band than releasing (unloading) it. What is the loop formed between the unloading and loading curves called?? A hysteresis loop. What is tensile stress?? The force applied per unit cross-sectional area of a material.

See Also [[Maths - Integration]]S Flashcards $$\int (x+2)^5 dx$$ What subsitution could you make in terms of $u$?? $$ u = x + 2 $$ If $u = x + 2$, what is $\frac{du}{dx}$?? $$ \frac{du}{dx} = 1 $$ If $u = x + 2$ and $\frac{du}{dx} = 1$, what is $dx$?? $$ du $$ $$\int (x+2)^5 dx$$ If $u = x+2$ and $du = dx$, how could you rewrite the integral?

See Also Flashcards What has the longest wavelength on the electromagnetic spectrum?? Radio waves What has the shortest wavelength on the electromagnetic spectrum?? Gamma rays What is the range of wavelengths for visible light?? $$ 380nm \text{to} 740nm $$ What is the speed of an electromagnetic wave in a vacuum?? $$ 3 \times 10^8 m/s $$ What do electromagnetic waves consist of?? Oscillating magnetic and electrical vibrations at right angles to one another. 2021-03-30 What is roughly the wavelength of radio waves?

See Also [[Maths - Differentiation]]S [[Maths - Product Rule]]S [[Maths - Chain Rule]]S Flashcards What is the Quotient Rule used for?? Finding the derivative of two things being divided. $$\frac{d}{dx}\left(\frac{u}{v}\right)$$ What is this equal to?? $$ \frac{v \cdot \frac{du}{dx} - u \cdot \frac{dv}{dx}}{v^2} $$ What is important you remember about the product rule?? The order. Where does the $v^2$ bit come from in the product rule?? It’s actually the product rule with $v^{-1}$, which goes to $\frac{1}{v^2}$