Can someone answer this math question?
2y+6x=3 subtract 6x from both sides 2y= -6x+3 divide both sides by 2 y = -3x + 1.5 this represents a linear equation because it is based on the equation: y=mx+b in y = mx+ b, y equals the y coordinate of a graph, m represents the slope, x represents the x coordinate, and b represents the y-intercept. because the slope is -3, the line will slope downward. remember, slope is rise over run, meaning that the top number is the number up or down, and the bottom number is the number to the left or right. -3 = -3/1, meaning that, in this case, your line will go down 3 units and to the right 1 unit.
How do I solve this math question?
First let's try to develop a general theory for these kinds of questions. So lets consider a general equation of Conic section which is [math]ax^2+2hxy+by^2+2fx+2gy+c = 0[/math]Rearrange this equation as [math]ax^2+2x(hy+f)+(by^2+2gy+c) = 0 [/math]Solving for the [math] x[/math] we have [math]x= \dfrac{-2(hy+f)\pm2\sqrt{(hy+f)^2-a(by^2+2gy+c)}}{2a} [/math]Now if we want that given equation should have linear factors then this also means that above expression should have linear relationship between [math]x[/math] and [math]y[/math]. Now for this to happen the term under square-root should be a perfect square.[math]\implies (hy+f)^2-a(by^2+2gy+c)[/math] should be perfect square Simplifying this equation and we will get [math](h^2-ab)y^2+2y(gh-af)+(g^2-ac) = 0 [/math]Now this equation will be a perfect square if it has only one root i.e it's discriminant is zero.[math]\implies 4(gh-af)^2 - 4(g^2-ac)(h^2-ab) = 0[/math] Simplify this and we will get [math]\boxed{af^2+ch^2+bg^2-2fgh-abc = 0}[/math] Hence this condition should be true if you want to factorize any such equation into two linear factor. More neat and aesthetic form to express this condition is [math] \begin{vmatrix} a & h & g \\ h & b & f \\ g & f & c \end{vmatrix} = 0 [/math]. This is also called discriminant of Conic section . (It decides whether the given equation represent an ellipse or parabola or circle or point or hyperbola or pair of straight line. Here it represents the pair of straight line).Now come to this particular equation. (I am changing [math]a[/math] to [math]P[/math] and [math]b[/math] to [math]Q[/math] to avoid confusion).So given equation is [math]3x^2 + 2Qxy + 2y^2 + 2Px - 4y + 1[/math]. If you compare this to standard form you will find that ,[math]a= 3 , h = Q , g = P , b = 2 , f = -2[/math] and [math]c = 1[/math] So discriminant of this equation is [math] \begin{vmatrix} 3 & P & Q \\ Q & 2 & -2 \\ P & -2 & 1 \end{vmatrix} = 0[/math]Solving and rearranging this we have ,[math]Q^2+4PQ + 2P^2 + 6 = 0 [/math]Clearly [math]q[/math] is a root of quadratic equation given by [math]x^2+4Px+2P^2+6[/math]
Can someone help me with this question?
you didn't italicize anything, but I'll assume it was the first sentence. That's a theory. The second sentence is an observation.
How does knowing complex math help someone?
I think in several waysThe thought processes of math can be applied in other, non-math, settingsOne tool of math is answer checking. In others settings it is good to practice thatvdiscipline.Sometimes in math less precise answers are obtained from approximations. In non-math problems that can also work. Having every last minute detail leads to analysis paralysis.On the emotional axis, knowing complex math leads to feeling good about yourself which is healthyApplication of math to advance an engineering or social solution can help others, which sends us back to #4
Can someone help me with GRE preparation?
A2AI am assuming that you already know the basic GRE guidelines,the test format,marking scale etc.1.Analytical writingBuy the official guide.The Official Guide to the GRE® revised General Test, Second EditionGo through the ETS guidelines for essay writing and read some sample essays when you are feeling bored.Just give them a simple reading and nothing else.Get to know the format and marking scale.Score Level DescriptionsIn last month try writing them with time constraint.You can choose topics from ETS website for their essay pool Analyze an Issue and Analyze an Argument.2. Verbal SectionFor Vocabulary you can download the Magoosh Free GRE Vocabulary Flashcards.This is the time to be smart in using the smartphone.This vocab is enough for GRE given the time constraint.Whenever you get time in office ,while commuting just open the app and revise as much as you can.Minimize the use of social apps.You can also use the Magoosh Gre Vocabulary Extension for chrome.Use Official GRE® Verbal Reasoning Practice Questions, Volume 1.Read few tricks given online to solve RC’s.Please practice them as much as possible.Try to solve 2 RC’s daily for first one on weekdays after your office. So in the next month you will be left only with practicing Sentence Equivalence questions which depend on your Vocabulary because by this time you must have covered most of you vocab part and it will be more fruitful now to practice them. Useful resources GRE Reading Comprehension - Winning Strategies - Magoosh GRE Blog , The Ultimate Guide to Destroy GRE Reading Comprehension - CrunchPrep GRE (This one is really good).Last two months practice the full Verbal section.Try learning vocab through Mnemonics.There is a website which lets you practice GRE words exactly in the order of Barron's wordlist. Does anybody know it?3. Quant SectionWhat will be the best books that can help in GRE maths?4. Test seriesTwo ETS tests.POWERPREP II SoftwareSix Manhattan Tests.Kaplan Test.5. If money is no constraint buy a Test Prep like Magoosh.6. Join a Faceboook group for GRE- Fall admission 2016–17 to remain updated regarding useful information.I think this will help.For resources ,they are already available online for free no need to spend large amount of money for it.These are completely my personal views so take whatever you feel is good for you.
I have dyscalculia. Can mathematics solve any question/theory out there? Can you convince me how beautiful Math is?
“ Can mathematics solve any question/theory out there? ”No. Indeed this very question proves the answer is ‘no’. Since this very question demands an answer that is beyond mathematics itself.Math however CAN solve very many problems and is essential for technology and science.-“I have a degree & an IQ of 138 ”I thought everybody on Quora has an IQ of at least 700 :DAnyway even people very bad at math are not necessarily stupid.-“Can you convince me how beautiful Math is?My memories of math in school have left me hating it with a passion!”Well that might depend on your teachers. Of course your dyscalculia factors in. Few people enjoy activities they suck at.Of course it does not mean you have no potential for math.In any case you might try to buy (or find online) books (or sites) that give “fun math problems” of different levels.-“Can you convince me how beautiful Math is?”Well math never lies and is absolute. In math things are either true or false. Even science is not that secure (I mean maybe what we know now in science is partially false, not so for math!)Math can help us discover different connections! For example we know that:[math]i = \sqrt{-1}[/math]So we have complex number of the form [math]z = a+b\cdot i[/math] (where a and b are regular numbers)Now that might seem just a trick to solve an equation where the square root is negative, but in reality complex numbers open up an incredible field that has very many applications, for example in electrical engineering.Math is all about solving problems! If you enjoy solving problems you enjoy math.In any case it’s not a crime not to love math. One might understand how important math is even if he himself dislikes doing it.
How can the reading theory of maths help in the JEE?
Questions asked in JEE are quite tricky compared to the questions asked in board exams. Especially in JEE Advanced, you need a lot of logical thinking to answer the questions. Understanding the theory behind every concept and topic will help in solving questions. You must also understand and practice the derivations of the formulas. But more than anything else, you need to practice. The more you practice, the better you get. So, as you finish a chapter, solve as many JEE Maths practice questions as possible.
Velocity and Net Change Math Calculus. Can someone help me with this last part?
I have most of this problem figured out. It is just one part that I can't get. It is just part e that I simply cannot get. The question says. A drag racer accelerates at a(t) =66 ft/s^2. Assume that v(0)=0 and s(0)=0. a. Determine and graph the position function for t ≥ 0. b. How far does the racer travel in 6 s? c. At this rate, how long will it take the racer to travel 1/3 mi? d. How long will it take the racer to travel 300 ft? e. How far has the racer traveled when it reaches a speed of 177 ft/s? The correct answer is 237.343. I got 230.1456. Thanks...
What math you must know to better understand control theories?
In order:Linear algebra (matrices, eigenvalues)Dynamical systems (stability)Complex analysis (complex roots, Cauchy theorem)Optimization (cost functional)Probability (stochastic processes)plus (for advanced topics)Differential geometry, Differential games, many more...