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Cos x cos y = 2 sin( (x y)/2 ) sin( (x y)/2 ) Trig Table of Common Angles;44 latex100{x}^{2}1000x{y}^{2}10y2425=0/latex 45 latex4{x}^{2}16x4{y}^{2}16y16=0/latex For the following exercises, use the given information about the graph of each ellipse to determine its equation 46 Center at the origin, symmetric with respect to the x– and yaxes, focus at latex\left(4,0\right)/latex, and point on3x 4y £ 100 (0, 25) (0, 0) 75 (x,y) z 6xy y2 (0,25) z 0 625,0 z 00 4 (0,0) z 00 = = æö ç÷= èø = z max = 625 at x = 0, y = 25 A 'R Insti', A 10 R N1, IPIA, Kota (Rasthan), INDIA wwwreliableko, E @reliableko 3 C (A) ARC 21 ATE (T I) 3 There are two dice each numbers as 1, 2, 3, 5, 7, 11 Find the probability that the sum of the
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X^2-y^2/100 factorise-Find stepbystep Calculus solutions and your answer to the following textbook question Find equations of the osculating circles of the parabola $$ y=1/2x^2 $$ at the points (0, 0) and (1, 1/2) Graph both osculating circles and the parabola on the same screenGiven Triangle abc, with angles A,B,C;



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Product How it works;Free Circle calculator Calculate circle area, center, radius and circumference stepbystep(100 3) Example 48 In bridge, a player is dealt 13 out of 52 cards How many possible bridge hands are there?
1/π x 2 y 2 < 1 f(x, y) = 0 x 2 2 y ≥ 1 (a) Compute the probability density function f X for X ANSWER ∞ 1 √ 2 1 − x 2 −1 ≤ x ≤−1 f X (x) = f(x, y)dy = π −∞ 0 otherwise (b) Compute the conditional expectation EXY = 5 ANSWER Probability√ √ de nsity for X given Y = 5 is uniform on (− 1 − 5 2, 1 − 5 2) So EXY = 5 = 0 (c) ExpressX,Y = meshgrid(x,y) returns 2D grid coordinates based on the coordinates contained in vectors x and y X is a matrix where each row is a copy of x, and Y is a matrix where each column is a copy of yThe grid represented by the coordinates X and Y has length(y) rows and length(x) columnsAnswer and Explanation 1 Become a Studycom member to unlock this answer!
Find the point where the tangent to the circle with equation \(x^2 y^2 = \) at the point (2, 4) crosses the xaxis Reveal answer Draw a diagram to show the circle and the tangent at theBack to Algebra Calculator » About us Who we are;For system of equations xy=8 and y=x2, check (correct) solution x=3, y=5 xy=8 and y=x2 @ x=3, y=5;




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SPAIN, ENGLAND, AUSTRALIA, MOROCCO Example 47 Compute the following binomial coe cients (100 0); Rated 4 out of 5 by SkipperDave from Twin and Earth at a Good Price I used the 25mm flat twin and earth Good cable and works well with standard cable strippers and terminals Used it for ring mains and the 25 double cable clips made light of the double drops to the sockets Date published Rated 5 out of 5 by Frank2309 from Value for money Value forEllipsoids are the graphs of equations of the form ax 2 by 2 cz 2 = p 2, where a, b, and c are all positive In particular, a sphere is a very special ellipsoid for which a, b, and c are all equal Plot the graph of x 2 y 2 z 2 = 4 in your worksheet in Cartesian coordinates Then choose different coefficients in the equation, and plot a




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Solution Determine Whether The Following Equation Defines Y As A Function Of X X 2 Y 100 Does The Equation X 2 Y 100 Define Y As A Function Of X
SOLUTION 13 Begin with x 2 xy y 2 = 1 Differentiate both sides of the equation, getting D ( x 2 xy y 2) = D ( 1 ) , 2x ( xy' (1)y) 2 y y' = 0 , so that (Now solve for y' ) xy' 2 y y' = 2x y, (Factor out y' ) y' x 2y = 2 x y, and the first derivative as a function of x and y is (Equation 1) To find y'' , differentiate both sides of this equation, gettingThe linspace function provides a convenient way to create uniformly spaced data with the desired number of elements The following statements produce vectors over the range of the random data with the same resolution as that generated by the 858 statement in the previous sinc example xlinTRANSFORMATIONS OF RANDOM VARIABLES 3 Let FY (y) denote the value of the distribution function of Y at y and write FY (y)=P(Y ≤ y) Z y 0 Z y −x 2 0 2e−x1 − 2x2 dx 1 dx2 Z y 0 −2e−x1 −2x 2y x 0 dx2 Z y 0 −2e−y x2 − 2x2 − −2e−2x2 dx2 Z y 0 −2e−y − x2 2e−2x2 dx 2 = Z y 0 2e−2x2 − 2e−y − x2 dx 2 (7) Now integrate withrespect tox2 asfollows FY (y)=P(Y




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Help with these questions would be greatly appreciated 7Two real numbers x and y are such that 2xy=100 Find the maximum value of the product of the two numbers 8 A cuboid has a square base of length x cm and height y cm (i) Express the volume V of the cuboid in terms of x and y (ii) Show that the surface area of the cuboid is 2x^2 4xy(x−a) 2 (y−b) 2 = r 2 The answer is to Complete the Square (read about that) twice once for x and once for y Example x 2 y 2 − 2x − 4y − 4Extended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music WolframAlpha brings expertlevel




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Econ 1A Ramu Ramanathan Spring 03 Answers to Exam #2 I Let X and Y be two random variables, with means µ x and µ y, Var(X) = 2 = E(X σX 2) − 2, Var(Y) = = E(Y µX 2 σY 2) − 2, and Cov (X, Y) = µY σXYNow make the transformations U = X Y, and V = X − Y (a) (3 points) Derive E(U) and E(V) in terms of µX and µY25(x 2) 2 4(y – 5) 2 = –100 100 100 = 100 The larger demoninator is a 2 , and the y part of the equation has the larger denominator, so this ellipse will be taller than wide (to parallel the y3 For each solution ( x,y,z,,µ), find f(x,y,z) and compare the values you get The largest value corresponds to maximums, the smallest value corresponds to minimums 5 Examples Example 51 Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints xy z =0and x2 2z2 =1 f(x,y,z



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Find the Center and Radius x^2y^2=100 This is the form of a circle Use this form to determine the center and radius of the circle Match the values in this circle to those of the standard form The variable represents the radius of the circle, represents the xoffset from the origin, and represents the yoffset from origin The center of the circle is found at Center These valuesSin ^2 (a) 0/4 1/4 2/4 3/4 4/4 cos ^2 (a) 4/4 3/4 2/4 1/4 0/4 tan ^2 (a) 0/4 1/3 2/2 3/1 4/0 ;News, email and search are just the beginning Discover more every day Find your yodel




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Example 14 The plane x y − z = 1 intersects the cylinder x 2 y 2 = 1 in an ellipse Find the points on the ellipse closest to and farthest from the origin We want the extreme values of f = x 2 y 2 z 2 subject to the constraints g = x 2 y 2 = 1 and h = x y − z = 1 To simplify the algebra, we may use instead f = x 2 y 2First, the expression needs to be rewritten as x 2 a x b x 2 To find a and b, set up a system to be solved ab=3 ab=1\times 2=2 a b = − 3 a b = 1 × 2 = 2 Since ab is positive, a and b have the same sign Since ab is negative, a and b are both negative TheNote General Form always has x 2 y 2 for the first two terms Going From General Form to Standard Form Now imagine we have an equation in General Form x 2 y 2 Ax By C = 0 How can we get it into Standard Form like this?




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A arbYorough is a hand whichPlease feel free to Ask MathPapa if you run into problems Related Articles Algebra Calculator Tutorial;The line y = (a^2)x and the curve y = x(b − x)^2, where 0




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So, for example, if y = cos 1 2 x then dy dx = − 1 2 sin 1 2 x 5 A simple technique for differentiating directly In this section we develop, through examples, a further result Example Suppose we want to differentiate y = ex3 Let u = x3 so that y = eu Differentiating du dx = 3x2 dy du = eu Quoting the formula again dy dx = dy du × du dx So dy dx = eu × 3x2 = 3x2ex3 We will nowX2 y2 = p x2 k2x2 Now f(x,y) = x2 k2x2 = (p x2 k2x2)2 So the crosssection is the "same" parabola as in the xz and yz planes, namely, the height is always the distance from the origin squared This means that f(x,y) = x2 y2 can be formed by starting with z = x2 and rotating this curve around the z axis Factorise x ^2 y^2/100 2 See answers Advertisement Advertisement veronika1 veronika1 Hii☺ Here is your solution☺ ===== To factorise x² y²/100 => x² ( y/10)² => ( x y/10 ) ( x y/ 10) ♦ Note a² b² = (a b) (a b) here this identity is used ===== Thanks☺ SerenaBochenek SerenaBochenek Answer Stepbystep explanation Given the expression we



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x2 y2 = 100, where the origin is our center since we have no h or k value We also know from √100 that we have radius 10 We can now graph this circle knowing we are centered at the origin, and we have a radius of 10 graph {x^2y^2=100 40, 40, , }Create your account View this answer The domain of the function f(x,y) = ln(x2 y2−100) f ( x, y) = ln ( x 2Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history



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Graph x^2y^2=100 This is the form of a circle Use this form to determine the center and radius of the circle Match the values in this circle to those of the standard form The variable represents the radius of the circle, represents the xoffset from the origin, and represents the yoffset from origin The center of the circle is found at Center These values represent the importantX = rand(100,1)*16 8;Differentiate (2x)^2100(yx^2)^2 Natural Language;




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Angle 0 30 45 60 90;If you don't include an equals sign, it will assume you mean "=0" It has not been well tested, so have fun with it, but don't trust it If it gives you problems, let me know Note it may take a few seconds to finish, because it has to do lots of calculations If you justX^2y^2=9 (an equation of a circle with a radius of 3) sin(x)cos(y)=05;




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The fact that some of the coeffi cients are functions of x should not slow us down Applying the quadratic formula we get y = ex ± (−ex)2 − 4 1 (−ex) 2 1 ex± √ 2 4 y = 2 Our original equation is valid only for y > 0, and √ e2x 4ex > √ e2x = e , so our final answer is ex √ 2 4 y = 2 2 xY = rand(100,1)*16 8;Example 2 if x = 10 and y is 4 (10 4) 2 = 10 2 2·10·4 4 2 = 100 80 16 = 36 The opposite is also true 25 a 4a 2 = 5 2 2·2·5 (2a) 2 = (5 2a) 2 Consequences of the above formulas (x y) 2 = (y x) 2 = y 2 2xy x 2 (x y) 2 = ((x y)) 2 = (x y) 2 = x 2 2xy y 2 Formulas for 3rd degree (x y) 3 = x 3 3x 2 y 3xy 2 y 3 (x y) 3 = x 3 3x 2 y




The Locus Of The Image Of The Focus Of The Ellipse Frac X 2 25 Frac Y 2 9 1 A B With Respect To Any Of The Tangents To The Ellipse Is A X 4 2 Y 2 100 B X 2 2 Y 2 50 C X 4 2 Y 2 100 D X 2




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R = sqrt(x^2 y^2) eps;A is opposite to A, b opposite B, c opposite C a/sin(A) = b/sin(B) = c/sin (Law of Sines) c ^2 = a ^2 b ^2 2ab cos b ^2SOLUTION 1 Let variables x and y represent two nonnegative numbers The sum of the two numbers is given to be 9 = x y, so that y = 9 x We wish to MAXIMIZE the PRODUCT P = x y 2 However, before we differentiate the righthand side, we will write it as a function of x only Substitute for y getting P = x y 2 = x ( 9x) 2 Now differentiate this equation using the product



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The points (x,y,z) of the sphere x 2 y 2 z 2 = 1, satisfying the condition x = 05, are a circle y 2 z 2 = 075 of radius on the plane x = 05 The inequality y ≤ 075 holds on an arc The length of the arc is 5/6 of the length of the circle, which is why the conditional probability is equal to 5/6 This successful geometric explanation may create the illusion that the followingThat is, if tones x, y, and z form a rising sequence of tones, then the measure of the interval from x to y plus the measure of the interval from y to z should equal the measure of the interval from x to z Such a measure is given by the cent, which divides the octave into 10 equal intervals (12 semitones of 100 cents each ) Mathematically, given tones with frequencies f 1 and f 2, theA 2 AB AB B 2 = A 2 B 2 Note AB = BA is the commutative property of multiplication Note AB AB equals zero and is therefore eliminated from the expression Check 100 is the square of 10 Check x 2 is the square of x 1 Factorization is (x 10) • (x 10) Equation at the end of step 1 (x 10) • (x 10) = 0 Step 2




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Once again I have some crazy relationship between x and y and just to get a sense of what this might look like if you plot all the X's and Y's that satisfy this relationship you get this nice little clover pattern and I plotted this off of Wolfram Alpha but what I'm curious about in this video is you might imagine from the title is to figure out the rate at which Y is changing with respect toY 2 − e x y − e x = 0 This is a second degree polynomial in y;ZdV where E is the portion of the solid sphere x2 y2 z2 ≤ 9 that is inside the cylinder x2 y2 = 1 and above the cone x2 y2 = z2 Figure 5 Soln The top surface is z = u2(x,y) = p 9− x2 − y2 = √ 9− r2 and the bottom surface is z = u1(x,y) = p x2 y2 = r over the region D defined by the intersection of the top (or 4




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Problem If you measure x as 100 § 6, what should you report for p x, with its uncertainty?For 3xy=18, check (correct) solution x=2, y=3 3xy=18 @ x=2, y=3;If the equation of an ellipse is given in general form p x 2 q y 2 c x d y e = 0 where p, q > 0, group the terms with the same variables, and complete the square for both groupings We recognize the equation of an ellipse if it is quadratic in both x and y and the coefficients of each square term have the same sign Topic Exercises Part A The Ellipse in Standard Form Given the




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The ellipse is in the form (x h)^2/a^2 (y k)^2/b^2 = 1 Where center = (h, k) focus = (h c, k), (h c, k) c^2 = a^2 b^2 x^2/100 y^2/64 = 1 => (x 0)^2/10^2 (y 0)^2/8^2 = 1 => center = (0, 0) c^2 = a^2 b^2 c^2 = 100 64 => c^2 = 36 => c = 6 => focus = (h c, k), (h c, k) => focus = (0 6, 0), (0 6, 0) => focus = (6, 0), (6, 0) I don't know how to get the eccentricity(1x2)5, (xy)(x2y)4, Example 46 How many arrangements are there of the letters in each of the following words?X 2 – 8x 16 y 2 4y 4 = 100 x 2 y 2 – 8x 4y = 100 x 2 y 2 – 8x 4y – 80 = 0 Keep in mind that there is no standard meaning to the term "standard form" If your book specifies some other form, memorize that form for your tests Find the center and radius of the circle with equation x 2 y 2 2x 8y 8 = 0




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Section 43 Double Integrals over General Regions In the previous section we looked at double integrals over rectangular regions The problem with this is that most of the regions are not rectangular so we need to now look at the following double integral, ∬ D f (x,y) dA ∬ D f ( x, y) d A where D D is any regionThe quadratic formula gives two solutions, one when ± is addition and one when it is subtraction x^ {2}2yxy^ {2}=0 x 2 2 y x y 2 = 0 This equation is in standard form ax^ {2}bxc=0 Substitute 1 for a, 2y for b, and y^ {2} for c in the quadratic formula, \frac {b±\sqrt {b^ {2X 2 y 2 = r 2 where r is the radius Dividing by r 2 we have x 2 y 2 = 1 r 2 r 2 for an ellipse there are two radii, so that we can expect that the denominators should be different Hence we have the standard form of an ellipse centered at the origin x 2 y 2 = 1 a 2 b 2 The points (a,0), (a,0), (0,b), and (0,b) are called the vertices of the ellipse Note Although we have written




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44 Solving simultaneous equations (EMA38) Up to now we have solved equations with only one unknown variable When solving for two unknown variables, two equations are required and these equations are known as simultaneous equationsSolution Use rule 3 with f(x) = p x, f0(x) = 1=(2 p x), so the uncertainty in p x is –x 2 p x = 6 2£10 = 03 and we would report p x = 100§03 We cannot solve this problem by indirect use of rule 2 You might have thought of using x = p x£ p x, so –x x = p 2 – p x p x 10/5/01 5 and – p x




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