❶AGE PROBLEM In three more years‚ Miguel’s grandfather will be six times as old as Miguel was last year. When Miguel’s present age is added to his grandfather’s present age‚ the total is68. How old is each one now? This exercise refers not only to their present ages‚ but also to both their ages last year and their ages in three years‚ so labelling will be very important. I will label Miguel’s present age as "m" and his grandfather’s present age as "g". Then m + g = 68. Miguel’s age "last year"
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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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The Form of Structural Equation Models Structural equation modeling incorporates several different approaches or frameworks to representing these models. In one well-known framework (popularized by Karl Jöreskog‚ University of Uppsala)‚ the general structural equation model can be represented by three matrix equations: However‚ in applied work‚ structural equation models are most often represented graphically. Here is a graphical example of a structural equation model: For more information
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What will you learn after completing the lab? -The experiment will introduce different level of precision and measuring to the appropriate decimal place and will be familiar with measurements and weight. 2. Write the symbols and equation used to make a dilute solution from concentrated or stock solution. - The concentration of substance is described as molarity and this can be expressed as – Molarity = moles of substance per liter of solution. 3. Write
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EXPERIMENT : - 2 EXPERIMENT Verification of Bernoulli’s Energy Equation THEORY For steady incompressible flow Bernoulli’s energy equation along a streamline is written as [pic] constant where [pic] = pressure‚ [pic] = velocity and [pic] = height from datum Purpose of this experiment is to verify this expression. In the special apparatus the pipe is tapered with the cross section decreasing in the direction of flow first and then
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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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Why It Couldn’t Be The short story Cold Equations by Tom Godwin takes place on a ship called EDS. The space cruiser is piloted by a man named Barton. He has an order of killing the stowaway who snuck onto the ship because the weight on the EDS is too much for the ship to handle. In the process of hunting down the stowaway‚ he realizes it was a young innocent girl named Marilyn. Once Barton understands what kind of person Marilyn is‚ he doesn’t kill her immediately because he knows her reasons were
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Accounting Equation ACC 300 June 24‚ 2013 Bennie Clark Accounting Equation Assets = Liabilities + Stockholder’s Equity is the basic accounting equation. Liabilities are a company’s legal debts or obligations that come from transactions or from business operations. Stockholder’s equity is capital received from investors in exchange for stock‚ retained earnings and donated capital. These two portions of the balance sheet added together make up the company’s assets‚ which represent ownership
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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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Backward Bending Slutsky Equation In the Labor Supply Model‚ consumer has a choice between consumption and leisure. If they were to reduce their leisure and allocate more time working‚ they will be able to consume more. The amount of labor and consumption are determined by the interaction of consumer’s preferences and budget constraint. In this model‚ the utility function to be maximized is U(C‚L)‚ where individual cares about consumption (C) and leisure (L). The utility function is subjected
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