Coordinate Systems: A point P is described by three coordinates ‚ in cartesian (x‚y‚z)‚ in cylindrical (r‚ ϕ ‚z)‚ and in spherical (r‚θ‚ ϕ )‚ as shown. A point is also defined by the intersection of three orthogonal surfaces‚ as shown. Cartesian Cylindrical Spherical Transformation from Cylinder to Cartesian Coordinates Transformation from Cartesian to Cylindrical: Transformation
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Universal Studios Advisory Board Recommendations for the pursuit of the production of programming in partnership with WWE Recently‚ we at Universal Studios have been approached by Mattel Toys to begin working on the production of a children’s program with the intent of marketing its World Wrestling Entertainment (WWE) action figures to children for their economic gain. While there may also be the opportunity for monetary gain for Universal Studios in such production‚ there are several legal
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A. Kincaid American Literature Essay “In Cold Blood” vs. “In cold Blood” Truman Capote’s novel “In Cold Blood” written in 1966 became such an American crime classic that it was turned into a novel immediately in 1967. The book and the movie follow the story of a murder in Holcomb‚ Kansas by Dick Hickock and Perry Smith. This great American crime novel was turned into a movie by director Richard Brooks. The movie follows the book step for step due to the writing style by Truman Capote. The novel
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The sun by definition is the star that is "the central body of the solar system‚ around which the planets revolve and from which they receive light and heat." This self-luminous star is not only the largest object in the solar system containing 99.8 percent of the total mass but is also a fundamental necessity to every human and living thing’s life. The position of the in relationship to the sun‚ Earth determines the time of the year or season. The problem states "assume that at this time of
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mathematics at a deeper level. Review of homogeneous equations The homogeneous constant coefficient linear equation an y (n) +· · ·+a1 y +a0 y = 0 has the characteristic polynomial an rn +· · ·+a1 r+a0 = 0. From the roots r1 ‚ . . . ‚ rn of the polynomial we can construct the solutions y1 ‚ . . . ‚ yn ‚ such as y1 = er1 x . We can also rewrite the equation in a weird-looking but useful way‚ using the symbol d D = dx . Examples: equation: y − 5y + 6y = 0. polynomial: r2 − 5r + 6 = 0. (factored):
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18 Math 070 Chapter 7 Rational Expressions and Equations (7.1) Sec. 7.1 Simplifying Rational Expressions To reduce an algebraic fraction: factor first‚ then cancel _____________________________. 1. 4w3 28w 2 2. 27 a 3 33 3. y 2 7 y 18 y2 6y 8 19 Math 070 Chapter 7 Rational Expressions and Equations (7.2) Sec. 7.2 Multiplying and Dividing Rational Expressions To multiply algebraic fractions: factor first‚ next cancel __________________________ and then
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Solving Exponential and Logarithmic Equations Exponential Equations (variable in exponent position) 1. Isolate the exponential portion ( base exp onent ): Move all non-exponential factors or terms to the other side of the equation. 2. Take ln or log of each side of the equation. • Make sure to use ln if the base is “e”. Then remember that ln e = 1 . • Make sure to use log if the base is 10. • If the base is neither “e” nor “10”‚ use either ln or log‚ your choice.. 3. Bring the power (exponent)
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of -1. Straight Lines: Equation of a straight line is y = mx + c‚ where m = gradient‚ c = y-intercept. The equation of a line‚ if we know one point and the gradient is found using: (y - y1) = m(x - x1) (If given two points‚ find the gradient first‚ and then use the formula.) Two lines meet at the solution to their simultaneous equations. Note: When a line meets a curve there will be 0‚ 1‚ or two solutions. 1. Use substitution to solve the simultaneous equations 2. Rearrange them to form a quadratic equation
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formulas for: a. 75.69% C; 8.80% H; 15.51% O; MW = 206 b. 59.0% C; 7.1% H; 26.2% O; 7.7% N; MW = 180 1. Write (a) complete-formula equation‚ (b) ionic equation‚ (c) net ionic equation for this neutralization reaction: KHSO4 (aq) + NaOH (aq) → ? 2. In each of the following cases‚ predict whether a reaction will occur‚ and‚ if so‚ write the net ionic equation for the reaction: a. ZnSO4 (aq) + BaS (aq) → ? b. NaHCO3 (aq) + Ca(OH)2 (aq) → ? 3. Assign an oxidation number to each atom in: a.
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Basic equations of fluid statics | | | | | | | | | | | | | | | | An equation representing pressure field P = P (x‚ y‚ z) within fluid at rest is derived in this section. Since the fluid is at rest‚ we can define the pressure field in terms of space dimensions (x‚ y and z) only. Consider a fluid element of rectangular parellopiped shape( Fig : L - 7.1) within a large fluid region which is at rest. The forces acting on the element are body and surface forces. | | Body force
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