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# Analytical Math Problems

Analytical Geometry :
Analytical Geometry is a unit of mathematics with study of coordinate system,conic section,circle,equation of line.

Analytical Math Problem

1.  What is the center of the circle x+ y- 4x - y + 5 = 0

a) (2,1) b) (3,2) c)  (2,$\frac{1}{2}$) d)  (3,$\frac{1}{3}$)

2.  Express $\frac{21}{27}$ in standard form

a) $\frac{7}{-9}$            b) $\frac{3}{5}$ c) $\frac{7}{5}$ d) $\frac{-7}{4}$

3. IF xy, is an even integer then value of x and y is

a)  odd b)  even c)  an irrational number d)  none of the above

4. Calculate the gradient of the line AB  (1,-5)  and (4,6)

a)  $\frac{12}{3}$   b) $\frac{11}{3}$ c) $\frac{21}{7}$  d) $\frac{-11}{3}$

5. If Eccentricity is equal to 1,then the conic is called as

a)  Parabola b)  Ellipse     c) Hyperbola    d) None

6. Find the distance between A (3; 4) and B (6; 7)

a)  √9 b)  √3 c) 3√2     d)  0

7. Find the equation of the line with gradient = –2 passing through A (3,7)

a)  y = 2x + 3 b)  y = -2x + 1   c)  y = 2x + 5       d)  y = 5x + 3

8. the point (–6; –2) and perpendicular to 3x + 2y = 6

a)  $\frac{2}{3}$   b)  $\frac{3}{2}$    c)  $\frac{2}{5}$ d)  none

9. In the given figure, C is the midpoint of AB. Calculate the value of x and y.

10. Find the midpoint of the line joining A(-6; 4) and B(2;-5)

a)  (-2,-5)   b) (3,2) c)  (5,3) d)  (2,7)

11. What is the equation of Parabola

12. What is the standard form of equation of ellipse

Analytic Geometry Formula:

Mid point formula: $\left ( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} \right )$

The distance formula is used to find the distance between two points A (x1 ; y1) and B (x2; y2)

AB = $\sqrt{\left ( X_{2}-X_{1} \right )^{2}+\left ( Y_{2}-Y_{1} \right )^{2}}$

The gradient of the line = $\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}}$

The equation of a straight line is given by y = mx + c

The equation of the perpendicular bisector  = y – y1 = m(x – x1)

Question:This was my girlfriend's extra credit problem last semester and no one in her class was able to solve it without using a calculator. Not even my girlfriend's aunt, who is a high school math teacher, was able to solve it. (7x - 2)^(1/3) + (7x + 5)^(1/3) = 3 I attempted both approaches in earnest and neither of them yielded anything I deemed useful. Thanks for the suggestions though.

Answers:Well, one answer is obviously 3/7, that can be found out just by looking upon the problem. Now, function x^(1/3) is monotone increasing (because f(x) is monotone increasing if f'(x)>0, and (x^(1/3))'=(1/3)x^(-2/3)>0), so (7x - 2)^(1/3), (7x + 5)^(1/3) and (7x - 2)^(1/3) + (7x + 5)^(1/3) are monotone increasing too, so the graphic of function f(x)=(7x - 2)^(1/3) + (7x + 5)^(1/3) can have only one point of crossing with any horizontal line, such as f(x)=3, and therefore it has only one salvation which is 3/7.

Question:What would be the absorbance of the gaseous ozone if its total pressure is doubled? This is a question from my professor. How to solve this problem? Thanks.=)

Answers:The Beer-Lambert Law states that absorbance is linearly proportional to the concentration of the ozone in your sample. So if the pressure is doubles, then so does the concentration. Absorbance doubles.

Question:I'm going back to school this fall and I plan on taking Calculus with Analytic Geometry I, II, III, instead of the other math classes like college algebra and calculus. I'm pursuing an engineering degree and that math class is required... (math is my worse subject.... 4 years ago) I dont remember much of the stuff at all really, but I'm thinking they teach you everything along the way anyway.. I dont remember everything from algebra or geometry either... But I plan on studying my butt off and working hard for a good grade so... Am I wasting my time for the inevitable F or no its a piece of cake and can be done no problem? Thanks all for your help and opinion~!

Question:Solve for this equation: (find the value of "v" for the given parameters) k(v^c)/(1-v) = 1. Parameters include 0 0. (So the fraction will always be +ve, and = 1). 'v' is the variable here, while 'c' and 'k' are given constants. For instance, if c = ln 4/ln 3, and if k = 91^(c-1), then, m = 27/91 exactly. ---- Good luck! oops.. I wrote 'm' by mistake; I meant v = 27/91! Nick - I know there are special cases - that's there in every math problem. And in the example I gave, 'c' was definitely not an integer ln 4/ln 3.. so I'm really not looking for an integer solution; I did not make that specialization - I'm looking for an analytical solution. I'm not sure if I should say thanks for trying :/ but the question, as you can see, is not asking for a 'specialized' case.. I did mention that if there was a specialized case (like the one I gave as an example), then of course it's easy to solve. You're kinda telling me back what I'm trying to say anyway =.= The thing is, there is a limit to this equation .. to the 'solution', I mean. And it is dependent on k, c. I would like to see if there's a way to find the limit, or something close to it for an approximation. It's basically solving m(x^d) + x = 1, where m, d are constants. I guess though - out of courtesy - thanks for your answer.

Answers:If k=0, there's no solution. Otherwise, multiply through by 1-v to obtain k v^c + v - 1 = 0. If c is an integer between -3 and +4 inclusive, then we can solve the polynomial by radicals. Otherwise, there's no reason to expect to be able to solve the equation for general c and k. Of course there will be particular lucky cases, like the one you cooked up: let w be whatever you want (strictly between 0 and 1) and take k = (1-w)/w^c; then v=w is a solution. In response to your reply, the answer is negative: unless c is one of those integers, there is no explicit, closed form solution. There is a (fairly) smooth solution, and, as you say, you can approximate it iteratively point by point, but it's just the inverse of the function given by k v^c + v - 1 = 0.

Analytic Epistemology :This clip discusses some of the schools of thought in contemporary analytic epistemology. First, the clip mentions Bertrand Russells dislike for the standard notion of what constitutes "knowledge" in philosophy, believing it to be to much too vague. Then there is a brief summary of GE Moore's "Proof of an External World" and his views on foundationalism. The clip then mentions Ludwig Wittgenstein's idea that "meaning is use" within social contexts, and that philosophical obstacles are really just miscommunication within "language games." Simply put, Wittgenstein thought that there were no such things as genuine philosophical problems, and that philosophy was merely a byproduct of linguistic misunderstandings. The clip then discusses the differences between foundationalism and coherentism and WVO Quine's notion of the seamless "web of belief." Quine was a strong proponent of the natural sciences, and thought that findings in the natural sciences could shed significant light onto age-old philosophical questions concerning the nature of the mind and knowledge. The clip then summarizes "The Gettier Problem" which challenged the Platonic definition of knowledge as "justified true belief," and then ends with definitions of internalism/externalism, and Alvin Goldman's causal theory of knowledge.

Maths 911 Grade 11 Analytical Geometry :Maths 911 Live Show Grade 11 Analytical Geometry:Gradient of a Straight Line Presenter:John Luis Executive Producer:Dylan Green