Explain How to write a polynomial equation in standard form with roots x= a, b, c?
y = (x-a)*(x-b)*(x-c) y = 0 for x= a or b or c now multiply out the factors y = (x-a)*(x^2 -(b+c)x +bc) y x^3 -(b+c)*x^2 +bc*x -a*x^2 +a*(b+c)*x +abc
Explain P(AUB)>= P(A)+P(B)?
This is not right. Suppose you have a bag of marbles and you pick one. Suppose that 5 are red and 5 are blue, and that 7 have green spots and the other three do not. Suppose A is the event that a blue marble is chosen and that B is the event that a spotted marble is chosen. Then P(A)=5/10 and P(B)=7/10. AUB is the event that the marble chosen is either blue or spotted (or both). Now if P(AUB)>=P(A)+P(B) then P(AUB)>=5/10+7/10=12/10, which is absurd. This is what is going on: In the event A we have a blue marble being chosen, which can be spotted or not. Since these are mutually exclusive events we can write that P(A)=P(A^B)+P(A^~B). A^B is the event that a blue spotted marble is chosen, and A^~B is the event that a blue, unspotted marble is chosen. Similarly for B we can write P(B)=P(B^A)+P(B^~A). AUB can happen in three ways: we can have a blue marble which is not spotted, a spotted marble which is not blue, or a blue spotted marble. Again the events are mutually exclusive so we can write P(AUB)=P(A^~B)+P(B^~A)+P(A^B). Now compare this to P(A)+P(B): P(A)+P(B)=[P(A^B)+P(A^~B)]+[P(B^A)+P(B... =P(A^~B)+2*P(B^A)+P(B^~A) P(A^B) is counted twice. So we have that P(AUB)=P(A)+P(B)-P(A^B) Since probabilities are always positive, we always have that P(AUB)<=P(A)+P(B)
How can I explain (a^2-b^2)-(a-b)=(a-b)(a+b-c)?
(a*a-b*b) - (a-b) = (a-b)*(a+b) - (a-b) = (a-b)*(a+b-1)(a-b)*(a+b-1)=(a-b)*(a+b-c)(a-b)*(c-1)=0If (a-b) is not equal to 0, c=1.If (a-b) is equal to 0, c is any number.
How do i write lengthy answers in BA exams?
BA exams are synonymous to essay like answers, especially the university papers. They consist of 4 questions of 15 marks each and it gets difficult to ‘think’ and write, rather, recollect the points and answer them in the same manner in the answer sheet. These may be some of the clichéd steps to follow, but they are helpful. Here’s what I do/follow: 1. As soon as you get the question paper from the examiner, go through all the questions carefully. Do not give them more than 10 minutes. Within 10 minutes, you need to know which answers are gonna be the content. 2. You start writing the answers. Once you start writing them, however the points are, their oder does not matter, as long as you have mentioned the necessary pointers and have explained them briefly. 3. Contrary to the popular belief, do not write unnecessary sentences and stretch the answer. Just write how much ever you know. The supervisors who correct your papers, they have lots of experience to catch which answer is genuinely explained in detail and which answer has ‘stories’. 4. All the answers should be given 30 minutes, if you have a time limit of 2 hours for a 60 marks’ paper. If you have more than 2 hours, utilize your time well. Go through the answers if you have spare time after attempting all of them. Highlight the main points with a pencil. 5. Last, but not the least, try to not acquire a doctor’s handwriting, towards the end of your paper. Maintain your pace and attempt each question’s answer on a new page of the answer booklet. All the best! :)
What is the simplest way to explain a+b whole square to a kid without using diagrams (squares)?
The easiest way to make a kid understand (a+b) while square or any identity for that matter, simply involves showing him the derivation by the multiplication ethod.You can surely make him understand that (a+b)wholesquared means (a+b)*(a+b)Now all you need to do is open the brackets and multiply each term of the first bracket to each term of the second bracket. For ex:(a+b)*(a+b)= a(squared)+ab+ab+b(squared)=a(squared)+2ab+b(squared)=(a+b)whole squared
How do I write the answers in engineering exams?
The person who evaluates hardly has 2 minutes for each paper evaluation. He doesn’t have much time to go through everything so you need to present in such a way that you score maximum of points irrespective of the matter written in those papers.I am talking only about theory externals and not internals. Remember these points whenever you write an exam.Always make sure that you present it in a neat manner. Avoid strikes and editing.Always answer those questions first which you know very well. You can write a movie story at last for the unknown answers. Just kidding. Don’t write stories.Write in paragraphs. Maintain 3–4 paragraphs for each answer. Never write an answer in points to explain an answer. If you write in points, the person who evaluates your answer sheet will count number of points and gives marks based on that.If there are any drawings/figures related to that question, draw them neatly and write a next paragraph which explains all about the figure. This gives you length to the answer.Tip: More drawings, more space, more marks.Use black/blue pen. Don’t use red or sketches. You are writing an answer not designing it.Sometimes even a 2 mark question can be asked for 10 marks. So you need to elaborate that.Tip: If you cannot explain a tree, tie a goat to it and explain the goat.If the question is about distinguish between the two, draw a neat table and distinguish them in points.For short answers, be simple and straight. no need to write lengthy paragraphs.For problems if you don’t know how to solve it, here is the tip. Read the question twice and write down the given data, some formulas related to question, and make some calculations related to that. Don’t write final result. Leave it.If you are proving a theory/formula and don’t know the steps or process, write down some formulas, make some calculations and finally write the final proving formula(which is already in the question) and write Hence Proved.This is just my version of dealing with exams. Although I prepare well and these tips are used by me in worst case scenario. All the time these helped me.As a matter of fact, I never failed in any of my engineering exams, not even once and now have a First Class Bachelor’s Degree in Mechanical Engineering.
Can I use 60 lines explaining my startup in my SOP for an admission in a US B-School?
First it is the GMAT that is the most important part of the application and work experience the least since some MBA students have no experience.SOP demonstrates accomplishment, and the accomplishment is that you have a successful startup. It is a one liner.
How do I write really long answers in university exams?
First rule : always make use of the question .For eg: what is the importance of heamoglobin?Answer should begin :Heamoglobin is very important.The importance of haemoglobin has been enlisted below.Then just mention the heading of the points:1.blood absorption2.heading 23.heading 3Etc... upto heading number n.Then one by one write the details of each point, like if I were to elaborate point 1 I would write it as 1.blood absorption The importance of haemoglobin in relation with blood absorption is blah blah blah....Do it for n points.Second rule : draw big diagrams and sketches For eg: Explain a dc motor. Answer : sketch big in size label each partThen list down each part like:1.armature2.feild coils... etc upto n points.Then write heading as construction and just express the sketch in words .then state working principles .then put heading as advantages list down advantages followed by disadvantages.lastly applications.Third rule: for questions like define economics?Start with origin of word economics,evolution of economics,throw light on father of economics,explain with an example as to how economics is used in daily life .Fourth GOLDEN rule: write in big fonts leave spaces between lines while changing a paragraph leave a blank line .