AskTheTask - Recent questions and answers
https://askthetask.com/qa
Potential inside a Conductor
https://askthetask.com/4025637/potential-inside-a-conductor
Imagine that you have a hollow spherical conductor carrying a net charge \(\displaystyle +Q\) that has inner radius \(\displaystyle R_1\) and outer radius \(\displaystyle R_2\). Now imagine again that you threw a point charge, \(\displaystyle +Q/2\), at the center of the sphere. Find the potential as a function of \(\displaystyle r\), the distance from the center, for \(\displaystyle 0https://askthetask.com/4025637/potential-inside-a-conductorFri, 01 Jul 2022 10:59:50 +0000Answered: Find multiple roots (repeated roots) of a polynomial depending on the real parameter "a"
https://askthetask.com/4025630/multiple-roots-repeated-roots-polynomial-depending-parameter?show=4025635#a4025635
topsquark said: Addendum: I know you already verified the equation but are you sure that last term isn't a \(\displaystyle a^3\)? Click to expand... Yes, absolutely sure.https://askthetask.com/4025630/multiple-roots-repeated-roots-polynomial-depending-parameter?show=4025635#a4025635Fri, 01 Jul 2022 10:59:50 +0000Chi-square for unknown mean and variance
https://askthetask.com/4025586/chi-square-for-unknown-mean-and-variance
I have a part of exercise solution, could someone explain me why here chi-square was used while mean and variance are unknown? I thought it can be used with known mean and unknown variance. Is it possible to use it?https://askthetask.com/4025586/chi-square-for-unknown-mean-and-varianceFri, 01 Jul 2022 10:59:49 +0000Answered: Dot and Dash Signals
https://askthetask.com/4025617/dot-and-dash-signals?show=4025624#a4025624
george357 said: Bayes' Theorem \(\displaystyle P(A | B) = \frac{P(B | A)P(A)}{P(B)} \) Where is P(AB)? Click to expand... Bayes' theorem is the trivial conditional probability relation: P(A & B)=P(A|B)P(B)=P(B|A)P(A)https://askthetask.com/4025617/dot-and-dash-signals?show=4025624#a4025624Fri, 01 Jul 2022 10:59:49 +0000Answered: calc practice help
https://askthetask.com/4025613/calc-practice-help?show=4025615#a4025615
i truly wish i knew. im guessing length times width times height?https://askthetask.com/4025613/calc-practice-help?show=4025615#a4025615Fri, 01 Jul 2022 10:59:49 +0000Answered: How to use change of variables here?
https://askthetask.com/4025611/how-to-use-change-of-variables-here?show=4025612#a4025612
I tag this question as "SOLVED"https://askthetask.com/4025611/how-to-use-change-of-variables-here?show=4025612#a4025612Fri, 01 Jul 2022 10:59:49 +0000Answered: Authentication in Pretty Good Privacy Confusions
https://askthetask.com/4025627/authentication-in-pretty-good-privacy-confusions?show=4025628#a4025628
Why not use sender's public key here? Click to expand... Because the public key is ... public. Anyone can obtain it and use it to encrypt a message. Why not use receiver's private key here? Click to expand... The sender does not have the receiver's private key. Only the receiver has it. It's ... private . Why not use receiver's public key here? Click to expand... Again anyone can obtain a public key. The whole idea behind this is that only the real source has access to the private key of the real source.https://askthetask.com/4025627/authentication-in-pretty-good-privacy-confusions?show=4025628#a4025628Fri, 01 Jul 2022 10:59:49 +0000Answered: Symbol Not Known
https://askthetask.com/4025605/symbol-not-known?show=4025610#a4025610
You should say you are generating the partial fraction representation. And it would appear you are correct, here is what Maxima says:https://askthetask.com/4025605/symbol-not-known?show=4025610#a4025610Fri, 01 Jul 2022 10:59:49 +0000Answered: Algebraic function
https://askthetask.com/4025589/algebraic-function?show=4025595#a4025595
Consider the function f(x) such that y = mx + c The definition of a linear function is βf(x) = f(βx) Substituting into left hand side βf(x) = βmx + βc Substituting into right hand side f(βx) = βmx + c So the linear function definition condition is not satisfied and the function y = mx + c is not linear. It is still a straight line and is called 'affine'. In science and some elementary maths this difference is too often ignored and the function called 'linear', because it is a straight line. This is why CaptainBlack asked for the definition of linear given to the OP. This distinction may appear nit picky and trivial, but it is the reason that Newton's Laws of Motion as usually stated do not obey The Principle of Relativity.https://askthetask.com/4025589/algebraic-function?show=4025595#a4025595Fri, 01 Jul 2022 10:59:49 +0000Answered: Mr. Jones
https://askthetask.com/4025576/mr-jones?show=4025585#a4025585
george357 said: The standard deviation is a way to measure the variation. For example, suppose we have a set of values of that variation. The higher the standard deviation, the further will be these values are spread out from the mean. To understand the idea visually, imagine that you have a standard normal distribution where the mean, zero, divides the distribution area equally. Now approximately 34.1% of the area will lie within a width equal to 1 standard deviation from one side of the mean. Click to expand... I felt like you copied and pasted that from somewhere. Do you understand what it is saying? For a "steadier" income, would you pick the lower or the higher standard deviation? Why?https://askthetask.com/4025576/mr-jones?show=4025585#a4025585Fri, 01 Jul 2022 10:59:49 +0000Answered: NEED HELP! PLEASE
https://askthetask.com/4025599/need-help-please?show=4025600#a4025600
dodhi said: how do you find the x and y intercept of y=(x+3)^3 Click to expand... What are the definitions of the y-intercept, and the x-intercept?https://askthetask.com/4025599/need-help-please?show=4025600#a4025600Fri, 01 Jul 2022 10:59:49 +0000Answered: Metrization of R^(omega)
https://askthetask.com/4025602/metrization-of-r-omega?show=4025603#a4025603
Going to give helping a college try. I didn't take differential geometry. I think using that \(\displaystyle x_n = 1/n\) converging to 0 is throwing us off, but I'll use it to work with an example. If you let \(\displaystyle x_{in} = 1/n\) then you have points such as \(\displaystyle a_1 = (x_{11}, x_{21}, ...) = (1, 1, 1, ...)\). B' = (-1, 1) x (-1/2, 1/2) x ... B'' = (-1, 1) x (-1, 1) x ... From here, $\Bbb R^{\omega}$ in the box topology is not metrizable , my initial reaction that it parallels Cantor's famous Diagonalization Proof was justified. B' is a construction to show that \(\displaystyle (a_n)\) cannot converge to 0 in the box topology. B'' bounds \(\displaystyle (a_n)\) and is a neighborhood of 0, but we need to show that "every neighbourhood of 0 contains all but finitely many points of the sequence." (Henno Brandsma from the link above) I think that's the key here. We only need to construct the counterexample B' to show there is at least one neighborhood that contains no point of the sequence \(\displaystyle (a_n)\)https://askthetask.com/4025602/metrization-of-r-omega?show=4025603#a4025603Fri, 01 Jul 2022 10:59:49 +0000Classifying Quadrilaterals
https://askthetask.com/4025569/classifying-quadrilaterals
Meanwhile, there is one more question that I am doubting myself. Some squares are parallelograms Some parallelograms are rectangles All squares are rectangles If the first two statements are true, the conclusion must be: a) True b) False c) Uncertain My answer was b) False, but the given answer is c) Uncertain. I thought that if some squares are rectangles, they definitely can't be all rectangles.https://askthetask.com/4025569/classifying-quadrilateralsFri, 01 Jul 2022 10:59:49 +0000Could you prove that f(A)>0 whenever A>0?
https://askthetask.com/4025561/could-you-prove-that-f-a-0-whenever-a-0
A is a 3x3 matrix. A is called positive, denoted A>0, if every entry of A is positive. Let $$f(x)=x^6 - x^3 + 1$$ Could you prove that f(A)>0 whenever A>0?https://askthetask.com/4025561/could-you-prove-that-f-a-0-whenever-a-0Fri, 01 Jul 2022 10:59:49 +0000Average score
https://askthetask.com/4025553/average-score
I need to solve this: Isobel’s class of 13 pupils all received an average of 85% on their history exam collectively. William scored 100%. If William is removed from the collective results, what would the new average be? My solution is: totalScore / 13 = 85 totalScore = 85*13 = 1105 I subtract William's score 100 from 1105 and divide it by 12 to get new average. (totalScore - 100) / 12 = newAverage (1105 - 100) / 12 = 1005 / 12 = 83.75 New average is 83.75%. Is this correct?https://askthetask.com/4025553/average-scoreFri, 01 Jul 2022 10:59:49 +0000logarithms in different form
https://askthetask.com/4025544/logarithms-in-different-form
HI; I am struggling to why this works log base z to the power 3 (32) = log base 2 (32) / 3. Thanks.https://askthetask.com/4025544/logarithms-in-different-formFri, 01 Jul 2022 10:59:49 +0000Matrcies representing the same linear transformation.
https://askthetask.com/4025542/matrcies-representing-the-same-linear-transformation
If \(\displaystyle T:V \to V\) is a linear transformation, and \(\displaystyle A\) is a matrix repredenting \(\displaystyle T\) with respect to the basis \(\displaystyle (e_1, e_2, \cdots e_n)\) and \(\displaystyle B\) is a matrix representing the same linear transformation \(\displaystyle T\) with respect to basis \(\displaystyle (u_1, u_2, \cdots u_n)\). Then, I want to ask what will be the relation between effects of these matrices on an element of \(\displaystyle V\). Let’s say \(\displaystyle T(x)=y\). Well, then we should have $$ A ~x = y = B ~x $$ But is that the case? I don’t think two different matrices multplied by same column vector will give out the same output.https://askthetask.com/4025542/matrcies-representing-the-same-linear-transformationFri, 01 Jul 2022 10:59:49 +0000Some Radicals
https://askthetask.com/4025532/some-radicals
$$\sqrt[3]{1+\sqrt{x}}=\sqrt{1+\sqrt[3]{x}}$$https://askthetask.com/4025532/some-radicalsFri, 01 Jul 2022 10:59:49 +0000Volts
https://askthetask.com/4025522/volts
I don't know under which math this belongs. It's electrical formulas. The problem says to use Watts Law but includes resistance in the Q. If Watts Law wheel is P=I×V but we have 4 categories on the hub.https://askthetask.com/4025522/voltsFri, 01 Jul 2022 10:59:49 +0000Looking for a specific recursion relation
https://askthetask.com/4025518/looking-for-a-specific-recursion-relation
I don't know how to do a search for information on a specific equation. It's \(\displaystyle f(n + 1) = 2 - \dfrac{d(n)}{f(n)}\), where d(n) is more or less arbitrary. It came up in some work I've been doing and I can't seem to get anywhere with it. Being non-linear it may not even have a closed form solution. There are two other ways to look at it. It's a non-linear difference equation: \(\displaystyle f \Delta f + f(f - 2) = d\) and it can also be considered as a continued fraction. (I'm going to be looking up that idea tonight.) Any thoughts? -Danhttps://askthetask.com/4025518/looking-for-a-specific-recursion-relationFri, 01 Jul 2022 10:59:49 +0000Train Station
https://askthetask.com/4025508/train-station
Two persons arrive at train station independently of each other at random times between 1 PM and 1:30 PM. What is the probability that one will arrive between 1 PM and 1:12 PM and the other between 1:17 PM and 1:30? Why is \(\displaystyle \frac{12}{30}\frac{13}{30}\) a wrong answer?https://askthetask.com/4025508/train-stationFri, 01 Jul 2022 10:59:49 +0000Help with a statistical investigation
https://askthetask.com/4025433/help-with-a-statistical-investigation
Hello! We are a group of engineering students who are performing a statistical survey and we would really like your help! Could you please answer this short survey (30 seconds) about guessing the weight of a chair from an image? It would help us very much. And please share it with your friends for a good cause! <a href="https://forms.gle/rRuc3jAgnqVTMo7v5" rel="nofollow">https://forms.gle/rRuc3jAgnqVTMo7v5</a> Best regards, fellow math-enthusiasts!https://askthetask.com/4025433/help-with-a-statistical-investigationFri, 01 Jul 2022 10:59:48 +0000Euclidean Geometry - Demonstration Exercise
https://askthetask.com/4025463/euclidean-geometry-demonstration-exercise
(a) Let be m a line and the only two semiplans determined by m. (i) Show that: If are points that do not belong to such , so and are in opposite sides of m. (ii) In the same conditions of the last item, show: and . (iii) Determine the union result , carefully justifying your answer. (b) Let be and 4 distincts points in a line such and . Show and . (c) Let be distincts points in a line m such . Under these conditions, show 2 distinct segments such the Union of both segments be equal to , carefully justifying your answer. Thanks for the help ^^https://askthetask.com/4025463/euclidean-geometry-demonstration-exerciseFri, 01 Jul 2022 10:59:48 +0000Mr. Norton
https://askthetask.com/4025499/mr-norton
Mr. Norton owns two appliance stores. In store 1 the number of TV sets sold by a salesperson is, on average, 13 per week with a standard deviation of 5. In store 2, the number of TV sets sold by a salesperson is, on average, 7 with a standard deviation of 4. Mr. Norton has a position for a person to sell TV sets. There are two applicants. Mr. Norton asked one of them to work in store 1 and the other in store 2, each for 1 week. The salesperson in store 1 sold 10 sets, and the salesperson in store 2 sold 6 sets. Based on this information, which person should Mr. Norton hire? At a glance, I would choose the person who sold more TV sets. But again, the answer would make no sense without proving. Can I assume that I have, for example, a normal distribution? I will calculate the area of both. The bigger the area, the better the selling, right?https://askthetask.com/4025499/mr-nortonFri, 01 Jul 2022 10:59:48 +0000Finding the eigenvector for eigenvalue =2.
https://askthetask.com/4025490/finding-the-eigenvector-for-eigenvalue-2
We have to find the eigenvalues and eigenvectors, and the dimension of eigenspace for this matrix: $$ \begin{bmatrix} 5 & -6 & -6\\ -1&4&2\\ 3 & -6 & -4\\ \end{bmatrix} $$ The eigenvalues are found to be 1, 2 and 2. The eigenvectors for \(\displaystyle \lambda=2\) will satisfy $$ A ~X = 2 X$$ Where \(\displaystyle X= (x_1, x_2, x_3)\) We will get three simultaneous equations, and all of them can be reduced (individually) to $$ x_1 = 2 (x_2 +x_3)$$ How can proceed from here? All I can think of is that Eigenspace of this eigenvalue will consist of all vectors of form \(\displaystyle t (y+z, y, z)\), that is \(\displaystyle x_2\) and \(\displaystyle x_3 \) are independent, thus making the dimension =2. But the answer is, eigenspace = \(\displaystyle t (2,2,-1)\) and dimension =1.https://askthetask.com/4025490/finding-the-eigenvector-for-eigenvalue-2Fri, 01 Jul 2022 10:59:48 +0000Funcional dependence and giving values for graph
https://askthetask.com/4025487/funcional-dependence-and-giving-values-for-graph
I have minimum, average and maximum values of something in columns. I have, for example, 24 values (I have a lot more). I am making a graph in Excel (funcional dependance) from minimum values and average values and from maximum values and average values. The graphs are plotted as Scatters and on the Scatters I am adding chart element Trendline (Polynomial with Order 6). From that Trendline I can get the functions (average function is the same). I have 2 functions for a case: 1. Case Minimum and Averages average function: y=0.0012x^6-0.0291x^5-0.1902x^4+10.253x^3-94.323x^2+315.61x-144.16 R^2=0.5326 minimum function: y=0.0024x^6-0.0846x^5+0.895x^4-0.425x^3-42.315x^2+210.33x-153.26 R^2=0.4506 2. Case Maximum and Averages average function: y=0.0012x^6-0.0291x^5-0.1902x^4+10.253x^3-94.323x^2+315.61x-144.16 R^2=0.5326 maximum function: y=0.0092x^6-0.4147x^5+7.0073x^4-55.137x^3+204.17x^2-312.59x+401.71 R^2=0.6944 My problem here is that for the same function I want to write one value for minimum and one for maximum and to get the graph for that values in the same graph form as now. It is somehow a prediction, I want to see for the same function if I got different minimum and maximum values what will I get. How can I do this in Excel? Thank you in advance. I will appreciate your answers.https://askthetask.com/4025487/funcional-dependence-and-giving-values-for-graphFri, 01 Jul 2022 10:59:48 +0000Two Fair Dice
https://askthetask.com/4025481/two-fair-dice
Two fair dice are rolled and the absolute value of the difference of the outcome is denoted by \(\displaystyle X\). What are the possible values of \(\displaystyle X\), and the probabilities associated with them. Finally a problem that does not lead to confusion. \(\displaystyle X = |6-0| = |0-6| = 6\) \(\displaystyle X= |6-1| = |1-6| = 5\) \(\displaystyle X = |6-2| = |2-6| = 4\) \(\displaystyle X = |6-3| = |3-6| = 3\) \(\displaystyle X = |6-4| = |4-6| = 2\) \(\displaystyle X = |6-5| = |5-6| = 1\) \(\displaystyle X = |6-6| = |6-6| = 0\) Is it correct to say that the probability to get any \(\displaystyle X\) is \(\displaystyle \frac{1}{7}?\)https://askthetask.com/4025481/two-fair-diceFri, 01 Jul 2022 10:59:48 +0000Sum of Floor(Sqrt(n)) for n=1 to n=1988
https://askthetask.com/4025475/sum-of-floor-sqrt-n-for-n-1-to-n-1988
This was taken from Brilliant Floor Function | Brilliant Math & Science Wiki \(\displaystyle S = \lfloor{\sqrt{1}}\rfloor + \lfloor{\sqrt{2}}\rfloor + ... + \lfloor{\sqrt{1988}}\rfloor\) Find the value of S. As usual, put answers in spoiler tags and show your work. This might be on the simpler side, but floor and ceiling functions don't get a lot of attention (at least in my experience)https://askthetask.com/4025475/sum-of-floor-sqrt-n-for-n-1-to-n-1988Fri, 01 Jul 2022 10:59:48 +0000Supply and Demand - limited goods
https://askthetask.com/4025467/supply-and-demand-limited-goods
Hi! I have to hold a presentation about the Supply and Demand curve. My question is: What happens to a curve, if the goods are very limited and the demand is very high? Thank youhttps://askthetask.com/4025467/supply-and-demand-limited-goodsFri, 01 Jul 2022 10:59:48 +0000How to perform F-test?
https://askthetask.com/4025375/how-to-perform-f-test
Im currently working on a statistical lab (analytical chemistry) and I am not sure how to chose which way to calculate the F-value. Initial thought was to calculate Spool for 2-11, and get F-calculated to then compare it to the F-table. The more I dove into the F-critical, F-calculated etc etc, the more confused I got. Im not sure at all how to go about this problem. Realising I probably misunderstood the whole concept of F-testing.https://askthetask.com/4025375/how-to-perform-f-testFri, 01 Jul 2022 10:59:48 +0000How can a 13 bit number represent 16 bit number?Or why is fragmentation offset multiple of 8?
https://askthetask.com/4025465/can-number-represent-number-fragmentation-offset-multiple
This is more of a mathematics confusion rather than a computer science confusion, so please treat it like that. I understand the computer science behind it(I hope so) but my confusion lies in the basic math part that is there. I am studying about ipv4 fragmentation. This is ipv4 header. The fields of concern here are-: -> identification(16 bit) -> Flags(3 bit) -> fragment offset(13 bit) -> Total length(16 bit) In order to understand these concepts of fragmentation, I have solved multiple problems. One of them is below. Here initially we have 5000 byte datagram of which 20 byte is header. The MTU is 1500 bytes. The answer is this-: But I am unable to realize this simple concept that I believe even a 5th grader can understand even though I am college level undergraduate student. It is being pretty shameful for me.I am leaving my shame aside and asking this instead of giving up. I have asked this everywhere and everyone says this is basic math but it is not clicking in my head. Imma memorize this lol. I can solve any numerical problem related to fragmentation but this curiosity isn’t letting me to learn further and go to ipv6. It would be immensely helpful to me if anyone can help me via that above example to understand this simple concept. I am unable to relate with this concept. I agree there are 2^13 offset values ie 0,1,2,3,4,5,6,7,8,9…..8191. So that is the total no. of fragments possible 8192 fragments. But datagram can be only as big as 2^16-1 bytes. But why are we dividing them? It doesn’t make any sense. Maybe it is trying to say that 8192 fragments need to span 65535 bytes which gives 7.99987793 as the answer. But I have calculated it later, and fragmentation doesn’t work like that. Opinion 1-: Max “true” fragment offset possible=sum of all previous DATA ONLY excluding header =65535-n*20 bytes. Where 65535 is the max total length possible.n is the number of fragments and 20 bytes is the header length The max value of offset possible is 8191. 65535-n*20 bytes should be represented by 8191 (both max values). But this opinion takes nowhere. Opinion 2-: Max. 13 bit number=8191 Max 16 bit number=65535 So 65535/8191=8.0000sthsth (not exactly 8). So the problem is like how can max offset value represent the max data size. But as i said in opinion 1, max data size can never be 65535 as header also takes up some space. Opinion 3–: Say i want to understand this example by a dummy example. Say fragmentation offset field is of 1 bit. And total length field is of 4 bit. What would happen? Here are some answers that I have read which gave me further confusions-: Why IP fragmentation is on 8 byte boundary? Cisco Learning Networkhttps://askthetask.com/4025465/can-number-represent-number-fragmentation-offset-multipleFri, 01 Jul 2022 10:59:48 +0000Solving polynomial equation coefficients (perhaps using Mathematica)
https://askthetask.com/4025455/solving-polynomial-equation-coefficients-perhaps-mathematica
I have recently been driving myself mad solving equations using falling factorials. A typical example would be \(\displaystyle n^5 = A n(n - 1)(n - 2)(n - 3)(n - 4) + B n(n - 1)(n - 2)(n - 3) + C n(n - 1)(n - 2) + D n(n - 1) + E n\) and finding A, B, C, D, and E. We can write this a bit more neatly as \(\displaystyle n^5 = A \dfrac{n!}{(n - 5)!} + B \dfrac{n!}{(n - 4)!} + C \dfrac{n!}{(n - 3)!} + D \dfrac{n!}{(n - 2)!} + E \dfrac{n!}{(n - 1)!}\) which saves some typing space for things like my graphing calculator or W|A. I have found a way to proceed but it gets quickly out of hand with larger n, which is the information I need to use to find a general formula for the coefficients. Now, since I know how to do them and have developed some expertise at it I have been working on how to get a computer to do the job for me. The best I've got is to plug it into Mathematica and have it simplify as much as I can. They I can choose a value for A. Then simplify. Choose a value for B. etc. This works and gets me a solution to the equation fairly easily but I am not quite satisfied with it. Is it possible to either use Linear Algebra (or something) to solve for the coefficients (or perhaps a matrix that can be solved) or is there a way to get Mathematica to do it for me? I don't know how to do either. Thanks! -Danhttps://askthetask.com/4025455/solving-polynomial-equation-coefficients-perhaps-mathematicaFri, 01 Jul 2022 10:59:48 +0000Some exponentials?
https://askthetask.com/4025403/some-exponentials
Find $x$, in closed form, that satisfies: $$ 2^x=5^{x+2} $$https://askthetask.com/4025403/some-exponentialsFri, 01 Jul 2022 10:59:48 +0000Hypotheses testing and the critical region
https://askthetask.com/4025438/hypotheses-testing-and-the-critical-region
Hello everyone! Could you please advise me how to solve this?https://askthetask.com/4025438/hypotheses-testing-and-the-critical-regionFri, 01 Jul 2022 10:59:48 +0000I know I need to form some kind of equation from geometry but I can't quite figure it out
https://askthetask.com/4025436/know-need-form-some-kind-equation-geometry-cant-quite-figure
Question is attachedhttps://askthetask.com/4025436/know-need-form-some-kind-equation-geometry-cant-quite-figureFri, 01 Jul 2022 10:59:48 +0000Level
https://askthetask.com/4025385/level
Got the right answer using a formula, but I don't know how to determine if the answer is going to be + or - I just took a guess. How do I properly determine if answer will be neg or pos? Formula is: T= rise x L / run Goal is to level a pump.https://askthetask.com/4025385/levelFri, 01 Jul 2022 10:59:48 +0000Remainder Computing
https://askthetask.com/4025428/remainder-computing
Hello, I was trying to solve the following exercises but I encountered some difficulties. Given the function \(\displaystyle f(x)=\frac{1}{1+x}\) compute the reminder when x = 1 and n = 5 using the following formula: \(\displaystyle Rn(a)=f(x)-\sum_{k=0}^{n}\frac{f^{(n)}(a)}{k!}\) I have already computed the derivates at point 1 but cannot get the correct result (which should be 1/2): \(\displaystyle f'(1)=-\frac{1}{4}\) \(\displaystyle f'(2)=\frac{1}{8}\) \(\displaystyle f'(3)=-\frac{1}{16}\) \(\displaystyle f'(4)=\frac{1}{32}\) \(\displaystyle f'(5)=-\frac{1}{64}\)https://askthetask.com/4025428/remainder-computingFri, 01 Jul 2022 10:59:48 +0000My challenge question -- Which side is larger?
https://askthetask.com/4025420/my-challenge-question-which-side-is-larger
\(\displaystyle 4^{\tfrac12} \ + \ 4^{\tfrac13} \ + \ 4^{\tfrac14} \ \ \ versus \ \ \ 5\) or, in other symbols, \(\displaystyle \sqrt{4} \ + \ \sqrt[3]{4} \ + \ \sqrt[4]{4} \ \ \ versus \ \ \ 5\) Without using a calculator or computer, please show the steps to determine it. Please hide your solution(s).https://askthetask.com/4025420/my-challenge-question-which-side-is-largerFri, 01 Jul 2022 10:59:48 +0000Which answer is correct out of the two answers?
https://askthetask.com/4025416/which-answer-is-correct-out-of-the-two-answers
Solution 1: The answer is$ \frac{2b^5\pi}{5} \times \left( 1 -\frac{a}{\sqrt{1+a^2}}\right)$ Solution 2: I want to decide which solution is correct? Would you help me in this task?https://askthetask.com/4025416/which-answer-is-correct-out-of-the-two-answersFri, 01 Jul 2022 10:59:48 +0000Blood Type
https://askthetask.com/4025410/blood-type
Kim has blood type O and John has blood type A. The blood type of their son Dan is O. What is the probability that John's genotype's is AO. Since Dan was mentioned in this problem, I will leave it to him to decide, do I attack the problem or he does?https://askthetask.com/4025410/blood-typeFri, 01 Jul 2022 10:59:48 +0000How to find
https://askthetask.com/4025448/how-to-find
how to know the gradient of the curve y=2x^3-6x^2+8x+1 is never less than2?https://askthetask.com/4025448/how-to-findFri, 01 Jul 2022 10:59:48 +0000Prove that if a>0, then there exists n∈N such that 1/n <a<n.
https://askthetask.com/4025394/prove-that-if-a-0-then-there-exists-n%E2%88%88n-such-that-1-n-a-n
Here is my solution: If we have two real numbers \(\displaystyle a\) and \(\displaystyle 1\), then by Archimedean property we have $$ a \lt 1 \times n_1 \\ a \lt n_1$$ Again, given two real numbers \(\displaystyle a\) and \(\displaystyle 1\), by Archimedean property we have $$ 1 \lt n_2 a \\ 1/n_2 \lt a $$ Let's take \(\displaystyle n = ~max~(n_1, n_2)\) we have $$ 1/n \leq 1/n_2 \lt a \lt n_1 \leq n \\ 1/n \lt a \lt n$$ Hence proved. Is my solution correct?https://askthetask.com/4025394/prove-that-if-a-0-then-there-exists-n%E2%88%88n-such-that-1-n-a-nFri, 01 Jul 2022 10:59:48 +0000Regular hexagon and its' diagnoal
https://askthetask.com/4025399/regular-hexagon-and-its-diagnoal
What the ratio beween the gray area to the white area? Given: Regular haxagon & diagnols of ithttps://askthetask.com/4025399/regular-hexagon-and-its-diagnoalFri, 01 Jul 2022 10:59:48 +0000Evaluating the integral having trigonometric functions using change of variables and jacobian
https://askthetask.com/4025352/evaluating-integral-trigonometric-functions-variables-jacobian
Evaluate $ \displaystyle\iint\limits_R \sin{(\frac{x+y}{2})}\cos{(\frac{x-y}{2})}dA$ where R is the triangle with vertices (0,0), (2,0) and (1,1). (Hint: Use the change of variables u = (x+ y)/2, v = (x− y)/2.) My attempt to answer: But when we plot sin((x + y)/2)*cos((x-y)/2), we get the below graph:https://askthetask.com/4025352/evaluating-integral-trigonometric-functions-variables-jacobianFri, 01 Jul 2022 10:59:47 +0000Countably subadditive in set function
https://askthetask.com/4025324/countably-subadditive-in-set-function
Hi, I'm not sure what the "countably subadditive" means by the formula, can anyone explain it clearly?https://askthetask.com/4025324/countably-subadditive-in-set-functionFri, 01 Jul 2022 10:59:47 +0000How did the author compute integration limits here?
https://askthetask.com/4025326/how-did-the-author-compute-integration-limits-here
Make appropriate changes of variables in the integral ∬R4(x−y)2dydx∬R4(x−y)2dydx where R is the trapezoid bounded by the lines x - y = 2 , x - y = 4, x = 0, y = 0. Write the resulting integral. My attempt to answer this question: u = x - y, v= x + y. x=12(v+u),y=12(v−u)x=12(v+u),y=12(v−u) $ J ( u, v) = \frac{\partial (x,y)}{\partial(u,v)} =\begin{vmatrix} \frac{\partial{x}}{\partial{u}} & \frac{\partial{x}}{\partial{v}} \end{vmatrix}$ = $\begin{vmatrix}\frac12 & \frac12 \\ -\frac12 & \frac12 \end{vmatrix}= \frac14 - (-\frac14) =\frac12$ Original integrand becomes $\frac{4}{u^2}$ Therefore, using the transformation T, the integral changes to $\displaystyle\iint\limits_R \frac{4}{(x-y)^2} dy dx = \displaystyle\int_?^?\displaystyle\int_?^? \frac{4}{u^2}\frac12 du dv$ Now, how to compute the integration limits?https://askthetask.com/4025326/how-did-the-author-compute-integration-limits-hereFri, 01 Jul 2022 10:59:47 +0000Six-Digit Numbers
https://askthetask.com/4025333/six-digit-numbers
How many six-digit numbers are there? How many of them contain the digit 5? Note that the first digit of n-digit number is nonzero. Does this question want to count all numbers between 100000 and 999999?https://askthetask.com/4025333/six-digit-numbersFri, 01 Jul 2022 10:59:47 +0000Tasks for matching the average with the standard
https://askthetask.com/4025343/tasks-for-matching-the-average-with-the-standard
9.27 In contract negotiations a company claims that a new incentive scheme has resulted in average weekly earnings of at least \$ 400 for all customer service workers. A union representative takes a random sample of 15 workers and finds that their weekly earnings have an average of \$ 381.35 and a standard deviation of \$ 48.60. Assume a normal distribution. a. Test the company’s claim. b. If the same sample results had been obtained from a random sample of 50 employees, could the company’s claim be rejected at a lower significance level than that used in part a?https://askthetask.com/4025343/tasks-for-matching-the-average-with-the-standardFri, 01 Jul 2022 10:59:47 +0000Grocery Store
https://askthetask.com/4025355/grocery-store
Albert goes to the grocery store to buy fruit. There are seven different varieties of fruit, and Albert is determined to buy no more than one variety. Hoe many different orders can he place? It is a confusing question. No more than one variety? He can place 7 orders in this case. Wrong logic maybe?https://askthetask.com/4025355/grocery-storeFri, 01 Jul 2022 10:59:47 +0000Discrete Textook
https://askthetask.com/4025365/discrete-textook
I'm running short on money (again) after buying a new cell phone and (finally) getting a new computer. I am looking for an online or downloadable (free) Discrete Math textbook. My web search has been somewhat miserable: I have found a couple but the topics vary greatly. I am specifically seeking information about how to solve difference equations (beyond the constant coefficient case) but would be interested in learning other topics that might come up in the book. Any thoughts? Thanks! -Danhttps://askthetask.com/4025365/discrete-textookFri, 01 Jul 2022 10:59:47 +0000