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PDF Editor FAQ

What are the ten songs that you listen to the most?

This was I2A (Inspired to Answer) by Mohit Arora.I am going to cheat and give my top ten in duodecimals ... base-12, which means I have twelve. But I still write it 10.NB: The letters A and B stand for 10 and 11 respectively.Here they are:10: Holiday Road by Lindsey Buckingham ... though it sounds cheery, the video contains an implied message that "being in Fleetwood Mac feels more like being in jail." It is well known from the National Lampoon family vacation film.LYNDSAY BUCKINGHAM - HOLIDAY ROAD - YouTube0B: Cloudless by Peter Gabriel ... this is unique, featuring an Australian aboriginal chant along with an amazing gospel group, the Blind Boys of Alabama.Peter Gabriel - Cloudless - YouTube0A: ᵜAzaɽa al-Ḣai by Rasha ... a beautiful Sudanese song with an unforgettable saxophone solo I cannot get out of my head.Rasha - Azara alhai - YouTube.flv - YouTube09: Tchuheten Betsemu ... when anyone asks me what songs have soul, I will always point to this one. I assume it is in Amhari.Tlahoun Gessesse - Tchuheten Betsemu (Ethiopiques Volume 17 ...08: Hallelujah by Nynke Laverman ... she is singing Cohen's classic in Frisian. Though I can only understand parts of the song, it is deeply in my bones. Mw. Laverman also has soul.Nynke Laverman & Ward Veenstra - Hallelujah - YouTube07: Sombre Reptiles by Brian Eno ... I always interpret this music as set on a river like the Congo, with whitewater rapids and palm trees ... and the dinosaurs look up.Brian Eno - Sombre Reptiles - Time Lapse - Four ...06: Night on Bald Mountain by Mussorgsky ... this is best known to Americans via Fantasia, the The Walt Disney Company (company) classic. Here is the original symphony, without the slow segue into "Ave Maria."Mussorgsky - Night on the bare mountain ...05: Stand Back [live] ... this was originally a Stevie Nicks solo song, but since 1987, she has given it to Fleetwood Mac. The 2004 version features an incredible drum solo, and Lindsey's guitar solo. I am glad to have seen it live.Fleetwood Mac/Stevie Nicks ~ Stand Back 2004 ...04: Dacw'Nghariad ... a Welsh folk song. It somehow gives me the chills.Rhos Male Voice Choir -- Music From The Welsh ...03: Kadus Kadus by the East West Ensemble ... what other song has a Jewish text in the archaic Geᵜez language. This song I find powerful and moving.Kabbalah Music - Kadus Kadus - YouTube02: Clouds Below Your Knees by Ray Lynch ... few people have heard of him. This represents some of his best work.Clouds Below Your Knees - Ray Lynch - YouTube01 Island of the Dead by Rachmaninov ... I consider this among the finest pieces of music ever composed.Rachmaninoff -The Isle of the Dead - Vladimir ...I hope you will agree this represents a diverse selection of music.

Where is Wales's most beautiful view and why?

As per the previous answers, Wales is liberally & literally littered with spectacular views from north to south, east to west.In my locale, however, the views around the coastal path on Cardigan Bay are quite something, with the added bonus of dolphins in the sea. Then there are the valley views en route from Tregaron up over Pontrhydfendigaid, heading to Ffair Rhos & out towards Llangurig, or even the Llanddewi Brefi to Ffarmers mountain road …Dozens to list, not enough time.

How can we make calculus-related math models?

I will assume you want to know how we can construct models that describes the real world, using calculus.The most used calculus part with regards to modeling is differential equation. DEs are equations that relate the rate of change of a function w.r,t some variable, with the function itself. Why is this useful though? Well, sometimes it’s better to relate the function with it’s derivative, because it’s easier then to grasp how the derivative evolves, and that is through the basis of the function outputs. For example, in biology, they observed that the growth of a population of bacteria is proportional to the bacteria population [math] P [/math], as in say there’s 1 bacteria, then it duplicates as we know, to 2 bacterias, then keep doubling to 4 then to 8 and so on. Put it in differential equations, it looks like a DE with the derivative as rate of change of population with time, related to the population itself:[math] \frac{dP}{dt} = kP [/math]where [math] k [/math] is some constant indicating how big this growth is i.e the ‘scale’ of the growthWe can solve this using techniques to get:[math]P=P_{0} e^{k t}[/math]where [math]P_0[/math] is the initial population at time = 0. We then have a model that describes the population of the bacteria over time.In the bacteria example we could deduce the solution i.e the population [math] P [/math] right away because we know by guts that it’s an exponential function due to how we keep multiplying the original population by a constant. We might not even need to construct a DE for it then. However, doing DEs is more convenient as we progress later on, when we want to describe something more abstract.For one of my math essays, I described how the density (how many car(s) per road unit length) of 2 lanes of traffic. It’s based on how if one lane has less cars at a point in time, drivers from the other lane will start to enter. Initially, there’s a “free-flow traffic density” function where we assume one lane goes by itself, corresponding to a rate of change in free-flow density wrt time. Once we consider cars from other lane moving in, that rate of change i.e derivative will increase because the amount of cars per unit road length will increase by time with that car influx, hence the free-flow traffic density will increase.[math] \left\{\begin{array}{l}{\frac{d \rho_{1}}{d t}=\frac{\rho_{o} a_{1}}{v_{\max } e^{-\rho_{1} / \rho_{o}}}+r_{1}\left(\rho_{2}-\rho_{1}\right)} \\ {\frac{d \rho_{2}}{d t}=\frac{\rho_{o} a_{2}}{v_{\max } e^{-\rho_{2} / \rho_{o}}}+r_{2}\left(\rho_{1}-\rho_{2}\right)}\end{array}\right. [/math]Just know that density is rho, and the subscripts of rhos indicate that of lane 1 or 2, whoever indicates.Put short, to make calculus-related mathematical models, try to relate something’s change to itself :)

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