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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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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In the poem “An Equation for My Children” by Wilmer Mills‚ the speaker wants to find out the relationship between his family life and mathematics. Initially‚ the speaker reveals his fascination with Pythagoras’ work‚ which inspired him to go on a quest to finding out how his family life revolved around Pythagoras’ complex theorems. Along the way‚ the speaker finds his investigation so elusive that it feels as if he asked Pythagoras himself to calculate the mathematical equation of a “music tuning
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The Drake Equation is used to estimate the number of civilizations in the universe. It is more of a tool to use and help us understand and figure out how many worlds are out there. Each of the terms are being multiply to get the outcome for N‚ which is the number of civilizations in The Milky Way Galaxy whose electromagnetice missions are detectable. According to SETI website‚ the Drake Equation values R*‚fp‚ ne‚ fl‚ fi‚ fc‚ L are defined as the following. In the first part of the equation is R*.
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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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06.05 Applications of Systems of Equations Part 1 1. Tony and Belinda have a combined age of 56. Belinda is 8 more than twice Tony’s age. How old is each? Tony’s age = t years‚ Belinda’s age = 56 - t years 56 - t = 2t + 8 56 - 8 = 2t + t ==> 3t = 48 ==> t = 16 years THUS Tony = 16 years‚ and Belinda = 40 years 2. Salisbury High School decided to take their students on a field trip to a theme park. A total of 150 people went on the trip. Adults pay $45.00 for a ticket and students pay
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Fairuz Dalilah Binti Abdul Rashid Are We Alone? : Discovering Life on Other Planets Habitable Zone and The Drake Equation A habitable zone‚ which is also known as the Goldilocks Zone‚ is basically a region where there is a probability in finding the extraterrestrial life. The finding is based on the temperature and the pressure of a certain planetary-mass objects. When the temperature is between 273K and 373K‚ there will be presence of water that can support the extraterrestrial life to live in
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