Sqrt 2 x sqrt 3 y

    • [PDF File]Maxima by Example: Ch.4: Solving Equations

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      4 Solving Equations Maxima has several functions which can be used for solving sets of algebraic equations and for nding the roots of an expression.

    • [PDF File]MATH 152 Problem set 6 solutions

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      2. 2 = 0 + 2 21 is of the form x2 + 2y2.So let’s consider odd primes only. A square of an integer is always 1 or 4 (mod 8). Hence x 2+ 2y can only equal 1, 3, 4, 6 (mod 8). Therefore primes 5 or 7 (mod 8) are not of form x2 + 2y2. Next we show that primes 1 or 3 (mod 8) are of the form x2 + 2y2. Lemma. p= 1 or 3 (mod 8) if and only if n2 + 2 0 (mod p) for some integer n.

    • [PDF File]Compression Members W-Shape - University of Alabama

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      Compression_Members_W‐Shape HW_3.1 Section: Material: Unbraced Lengths: Qs 1.000 W16x26 A992 - - Buckling about - - Qa 0.921 A 7.68 in 2 Fy 50 ksi X-axisY-axis Q 0.921 bf/2tf 7.97 Fu 65 ksi K 2.0 1.0 h/tw 56.8 E 29000ksi Lu 20 5 ft Fcr_NSE 32.5 ksi d 15.7 in r 6.26 1.12 in Fcr_WSE 31.0 ksi kdes 0.747 in KL/r 76.7 53.6 = K * Lu*12 / r Fcr 27.9 ksi tw 0.25 in rx 6.26 in Pn 214 k

    • [PDF File]p Example 7.8 0). p Solution. D p - Michigan State University

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      D2 = (x 3)2 + y2 = (x 3)2 + (p x)2 = x2 5x+ 9 We want to minimize D, since we are looking for the closest point. So we need to nd critical points of D. Di erentiating both sides (using implicit di erentiation), we get 2DD0= 2x 5 Solving this for D0, we get D0= 2x 5 2D = 2x 5 2 p x2 5x+ 9 This is zero when x= 5 2, so this is a critical point (in ...

    • [PDF File]Review Problems - Department of Mathematics

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      3. Sketch the solid whose volume is represented by the integral: Z ⇡ 2 0 Z 3 1 r2 sin( )drd 4. Evaluate the sum of integrals: Z 0 p3 2 Z y p 9y2 yx3 dxdy + Z 3 0 Z p 9y2 p 9y2 yx3 dxdy 5. Calculate the mass of the lamina with density ⇢(x,y)=x2 and shape bounded by x = y2 and x =4. r Lrsince = y n

    • [PDF File]Square Roots via Newton’s Method - Massachusetts Institute of Technology

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      be equivalent to Newton’s method to find a root of f(x) = x2 a. Recall that Newton’s method finds an approximate root of f(x) = 0 from a guess x n by approximating f(x) as its tangent line f(x n)+f0(x n)(x x n),leadingtoanimprovedguessx n+1 fromtherootofthetangent: x n+1 = x n f(x n) f0(x n); andforf(x) = x2 ...

    • [PDF File]MIPT, spring camp 2016, day 2 Theme: sqrt-decomposition

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      2. Sqrt decomposition on strings2 3. Sqrt decomposition on array3 4. Sqrt decomposition on array: split & rebuild4 5. Sqrt decomposition on queries6 1/6. 1. Sqrt decomposition on tree ... Erase(i) erase -th element of the arra.y 3. Sum(l,r,x) calculate sum of elements greater than on the range [ , ]. 4. Reverse(l,r) reverse the range [ , ].

    • [PDF File]Chapter 5 4ed - St. Bonaventure University

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      20 Chapter 5: Solved Problems Problem 19 Script File: F=[0 13345 26689 40479 42703 43592 44482 44927 45372 46276 47908 49035 50265 53213 56161]; L=[25 25.037 25.073 25.113 25.122 25.125 25.132 25.144

    • [PDF File]Sage Quick Reference: Calculus Integrals R f x dx integral(f,x) = f ...

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      minimize(x^2+x*y^3+(1-z)^2-1, [1,1,1]) Multivariable calculus Gradient: f.gradient() or f.gradient(vars) (x^2+y^2).gradient([x,y]) Hessian: f.hessian() (x^2+y^2).hessian() Jacobian matrix: jacobian(f, vars) jacobian(x^2 - 2*x*y, (x,y)) Summing in nite series X1 n=1 1 n2 = ˇ2 6 Not yet implemented, but you can use Maxima: s = ’sum (1/n^2,n,1 ...

    • [PDF File]DO NOW: SHOW ALL NEEDED WORK IN YOUR NOTEBOOK.

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      a) Find the differential dy when dx 0.01 and x 2, if y x x 5 34 . EXPLAIN what you’ve found. b) Find the differential dy when dx 0.2 and x 1, if y x x 2 sin( ) . EXPLAIN what you’ve found. c) Without a calculator, use differentials to approximate 4.2 .

    • [PDF File]Building Java Programs - University of Washington

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      // A Point object represents an (x, y) location. public class Point {private int x; private int y; public Point(int initialX, int initialY) {x = initialX; y = initialY;} public double distanceFromOrigin() {return Math.sqrt(x * x + y * y);} public int getX() {return x;} public int getY() {return y;} public void setLocation(int newX, int newY) {x ...

    • [PDF File]Finding Square Roots Using Newton’s Method - University of Pennsylvania

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      Applied to compute square roots, so f(x) := x2 −A, this gives xk+1 = 1 2 xk + A xk . (1) From this, by simple algebra we find that x k+1 −xk = 1 2xk (A−x2). (2) Pick some x0 so that x2 0 > A. then equation (2) above shows that subsequent approxi-mations x1, x2, ..., are monotone decreasing. Equation (2) then shows that the sequence x1 ...

    • [PDF File]EULER ANGLES AND 3D ROTATIONS BY MATRIX METHODS

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      [-1,-1,-1] [-1,0,sqrt(2) [0,0,-sqrt(3)] A practical application of the results in this table is finding the angle a support column should be cut to fit a cube snugly under conditions where the cube’s diagonal points straight upward.

    • [PDF File]Math 121 Homework 5 Solutions

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      x p 2 p 5 x p 2 + p 5 x+ p 2 p 5 x+ p 2 + p 5 : This equals x4 14x2 + 9: To show that this is the minimal polynomial, it is su cient to show that it is irreducible over Q. None of its roots are in Q, so if it is reducible, it splits as two quadratic factors. One of these will have p 2 + p 5 as a root. Hence one of the quadratic factors is one ...

    • [PDF File]The Normal Distribution and the Central Limit Theorem

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      Integrate[ E^(-x^2), x] 1 2 π Erf[x] Even though the integral of e-x2 can not be expressed in terms of elementary functions, it is possible to show that ∫-∞ ∞e-x2 ⅆx = π . Therefore 1 π e-x2 is a probability density function. It has mean 0 because its graph is symmetrical about x = 0. The variance is 1 π ∫-∞ ∞x2 e-x2 ⅆx.

    • [PDF File]sqrt{b^2} - American Mathematical Society

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      3 According to one anecdotal report, the appearance of the same notation differed in two chapters input by different individuals; the system used for that project was one in which the positioning of symbols in displays was manually adjusted by the person doing the input.

    • [PDF File]Solutions to Week 2 Homework

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      2.2.14. y0= xy3(1 + x2) 1=2; y(0) = 1 (a) Find the solution of the given initial value problem in explicit form. First, separate the variables: y 3 dy= x p 1 + x2 1=2 dx: The integral of the left-hand side is y 2 2 + C. There are a few ways to integrate the right-hand side. One is to make the substitution u= x2; du= 2xdx:

    • [PDF File]Volumes by Cylindrical Shells: the Shell Method

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      by y = x3, y = 0, and x = 2, about the line x = 3. The axis of rotation, x = 3, is a line parallel to the y-axis, therefore, the shell method is to be used. The height of the shell is f(x) = x3, 0 ≤ x ≤ 2; and the radius is 3 − x (as measured from the axis of rotation: when

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