What is the difference between these two graphs?
The graphs are the same, unless you have an old-school type teacher. y = Arcsin (x) (with an uppercase A) is sometimes used to represent the function with a restricted range. That is, y = Arcsin(x) is called "the principal arcsine of x" where x is in the interval [-π/2, π/2] and y must be in [-1, 1]. the other arcsine (with the lower case a) is the graph with no restrictions on the y value. It is not a function, but it is a relation. so, if you have a really "old-school" teacher, then the difference is that one graph is one-to-one and the other is not. good luck
What is the difference between tree search and graph search?
In Graph Search you hold a list of explored nodes, while in Tree Search you don't!when you have undirected cycled graph,these two searches produce different outputs because in Graph Search you know which node has been explored(visited) and then you don't expand it, but in Tree Search you don't know and you expand it again.but this doesn't mean Tree Search is dumb because it doesn't hold such list.sometimes for example in games you have repeated states and you have to explore them again.You can see pseudo code of both graph and tree searches in page 4 and 5 of this pdf:https://courses.cs.washington.ed...
What is the difference between a histogram and a bar graph?
The Difference Between Bar Charts and HistogramsHere is the main difference between bar charts and histograms. With bar charts, each column represents a group defined by a categorical variable; and with histograms, each column represents a group defined by a quantitative variable.One implication of this distinction: it is always appropriate to talk about the skewness of a histogram; that is, the tendency of the observations to fall more on the low end or the high end of the X axis.With bar charts, however, the X axis does not have a low end or a high end; because the labels on the X axis are categorical - not quantitative. As a result, it is not appropriate to comment on the skewness of a bar chart.Test Your UnderstandingProblem 1Consider the histograms belowWhich of the following statements are true?I. Both data sets are symmetric. II. Labels on the X axis are quantitative.(A) I only (B) II only (C) I and II (D) Neither is true. (E) There is insufficient information to answer this question.SolutionThe correct answer is (C). Both histograms are mirror images around their center, so both are symmetric. With bar charts, the labels on the X axis are categorical; with histograms, the labels are quantitative. Both of these charts are histograms. Therefore, their labels are quantitative.
What is the difference between arcsine and Arcsine?
'Arcsin' (equivalent to 'Sin ^-1' ) is the function with the restricted range of -pi/2 -> pi/2, while 'arcsin' (equivalent to 'sin^-1' ) has no restrictions. A standard procedure for multivalued functions is to use a lowercased version to indicate the multivalued variant and an uppercase version to indicate the 'principal branch', which is usually defined along with the function. Different functions have different principal branches. Here are a few straightforward ones for result in the form x + iy: Arcsin(z): -pi/2 <= x <= pi/2 Arccos(z): 0 <= x <= pi Arctan(z): -pi/2 < x < pi/2 Log(z): 0 <= y < 2pi
What is the difference between interpolation and extrapolation?
The simplest way to imagine it is to think of two data points on a graph. Interpolation would be to guess a new data point that would be *in between* the two data points. But extrapolation would be to guess the *next* data point that would come after those two.
What is the difference between position time graph, distance time graph and displacement time graph?
As far as I know, a position-time and displacement-time are exactly the same thing - though you could be using a slightly different definition.A displacement time graph simply shows where an object is at a given time. Consider a train on tracks - let's let 'X' be the distance from the end of the tracks. As the train leaves the station, X increases. The rate of increase depends solely on how fast it is going (steeper=faster). After an hour, the train stops (so the graph goes flat) and then goes back to where it started. At the point in the graph, the displacement goes DOWN - as the distance from the end of the tracks is now decreasing (since the train is returning home). When the train reaches home, the displacement is zero.A distance-time graph, in essence, doesn't care in what direction the train is travelling. It does not give a unique answer to "where is the train at time X" - only how far it has driven. Imagine the train simply driving forward 1m, then backwards 1m, for 10 minutes. Ignoring acceleration time, this would be indistinguishable from the train simply going straight on for the same length of time. A distance time graph can never go back to zero - it is always increasing.Hope this helps!
What is the difference between Linear and exponential functions?
“Linear function” can mean a couple of things. But in the context of high-school-level algebra, the basic ideas are like this:A linear function is one that is changing at a constant rate as [math]x[/math] changes.An exponential function is one that changes at a rate that's always proportional to the value of the function. A simple example is population growth for a very simple kind of organism, like bacteria. The larger the population is, the more the population will increase. (This is also assuming that the population hasn't gotten too large for its habitat.)That might not seem so clear, but the difference between them might be easier to see if you look at the values of [math]f(0), f(1), f(2), f(3),[/math] and so on.First let's look at the general formulas:Linear: [math]f(x) = ax + b[/math]. (You'll probably often see it as [math]f(x) = mx + b[/math], but let's stick with [math]ax + b[/math] so we can see the parallels between these concepts more easily.)Exponential: [math]f(x) = ba^x[/math], where [math]a[/math] is a positive number other than [math]1[/math].When you look at the linear function and compare [math]f(0), f(1), f(2), f(3), \ldots[/math], you may notice that when you add [math]a[/math] to [math]f(0)[/math] you get [math]f(1)[/math]. When you add [math]a[/math] to [math]f(1)[/math] you get [math]f(2)[/math]. When you add [math]a[/math] to [math]f(2)[/math] you get [math]f(3)[/math], and so on. Each time you increase [math]x[/math] by [math]1[/math], [math]f(x)[/math] gets [math]a[/math] added to it.(In this case, [math]f(0), f(1), f(2), f(3), \ldots[/math] form what we call an arithmetic sequence.)The exponential function has a related idea going on. When you multiply [math]f(0)[/math] by [math]a[/math] you get [math]f(1)[/math], and it goes on like that.(In this case, [math]f(0), f(1), f(2), f(3), \ldots[/math] form what we call a geometric sequence.)Another thing you might notice, from playing around with these different functions, is that in both cases, [math]b[/math] is the “starting” value. In other words, [math]f(0) = b[/math].
L x l = x l x l = -x explain?
(hint: use the "pipe" character | instead of the letter l, that will be less confusing - it's usually above the \ key on a standard keyboard, but is sometimes in other positions.) Sometimes it's useful to have an idea of the size of a number, without caring whether it's positive or negative. For instance, you may be interested in knowing how accurate some prediction is, withouth worrying about whether it was above or below the actual result. The absolute value function |x| is designed for this purpose. |x| is defined, as you said, as x if x is positive (or zero) and as -x if x is negative. This has the effect of stripping off any negative sign that is present, so |3| = 3 and |-3| = 3. It should be easy enough to see that regardless of whether x is positive or negative, |x| = |-x|. You should also be able to see that |x| could also be defined as sqrt(x^2). I'm not sure if your title represents an actual problem you're having trouble with, but if so, here's how to do it. Note that a = b = c means that a = b and b = c (and therefore also a = c). Verifying any two of these equations implies the third. Suppose |x| = x |x| = -x. The easiest equality to start with is |x| = -x. If this is true, then x must be negative or zero, and x |x| = x (-x) = -x^2. This then gives -x^2 = -x which means that x = 0 or x = 1. But x is negative or zero, so the only solution is x = 0.
What is the difference between true stress strain and engineering stress strain diagram.?
True stress and Engineering stresses are a bit different. Consider the figure showing stress-strain relationships of a mid-steel.**image source-R.C.Hibbeler-Mechanics of Materials 8th EditionThe above figures are the stress vs. strain graph of a mild steel in a tension test experiment.Now, Before doing the tension test we have to determine the length and diameter of the specimen and we assume these parameters remain constant throughout the whole experiment. So when we calculate the stress by the formula-we actually calculate the stresses (corresponding to different strains) for the given value of diameter which we have calculated in the beginning of experiment. These stresses are called Engineering Stresses. This is indicated by the lower portion of the graph in the above figure.but as we do the experiment we observe a phenomenon called necking and till now we have been neglecting any such necking which takes place. So let's see what happens when there is necking.**Source-google imagesSo, As we can see as the bar is subjected to tensile forces just like what happens in a tension test experiment and after certain instant a neck like region forms. This shows the cross-section of the specimen has changed as the experiment proceeds further.Hence whatever we will get the stresses now will be different from the ones we got when we we assumed the cross-section remained constant. These stresses are called TRUE STRESSES. True stresses are thus force divided by the area of the section at that instant. It can be shown by the upper curve in the stress-strain diagram above.(It should be noted that only after the necking starts there is a considerable change in the cross-section and thus the variation between the two stresses becomes more prominent).