where m0 is the rest mass of the particle and c is the speed of light in a vacuum. Find the inverse function of f and explain its meaning. Solution. We simply solve for v: m= m0 1− v 2 /c2 =⇒ m 1 − v 2 /c2 = m0 =⇒ m2 1 − v2 c2 = m2 0 m2 v2 =⇒ 1 − 2 = 0 c m2 =⇒ v2 m2 =1− 0 c2 m2 m0 m m0 m 2 =⇒ v 2 = c2 1 − 2 =⇒ v = ±c 1 − Our new function v(m) gives velocity v as a function of m. In particular‚ v(m) gives the velocity (as measured by a relatively stationary observer) that
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Inverse In this week’s assignment‚ I will be solving functions with different values and variables. Many companies and businesses‚ use these methods to either make progress or to change something that will benefit their success. The first function is: (f – h)(4) f(4) – h(4) I multiplied 4 with each variable. f(4) = 2(4) + 5 The x is replaced with 4. f(4) = 13 I used the order of operation to evaluate this function. h(4) = (7 – 3)/3 I will repeat the steps that I used
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repayment schedule is calculated on a $170‚000 loan but the net amount the borrower receives is only $163‚200. What is the effective annual interest rate charged on such a loan assuming loan repayment occurs over 156 months? Assume the interest rate is .75% per month. (Do not round intermediate calculations. Round your answer to 2 decimal places.) | Effective annual interest rate | % | 3) Suppose you take out a $1‚000‚ 4-year loan using add-on interest with a quoted interest rate of 23.25%
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and Logarithmic Functions 2.2 Logarithmic Functions MATH14 • Logarithmic Function with base b • Graph of Logarithmic Function • Natural Logarithmic Function • Properties of Logarithmic Functions • Exponential and Logarithmic Equations Logarithmic Function with base b Definition: The logarithmic function with base b is the inverse of the exponential function with base b. y logb x Note: Dom f if and only if x b y Rng f Logarithmic Function with base b Examples:
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Critical assessment of annual report of Wm Morrison Supermarkets Plc Word count: 1711 words Table of Contents Introduction 3 1.0 Overview of the Annual Report of Morrisons 4 2.0 Performance and Strategy Review 4 3.0 Governance 7 4.0 Reliability of the Annual Report of Morrison 8 5.0 Conclusion 8 References: 9 Introduction An annual report is a portrait of the business of a firm. In fact‚ it is the most important way for a company to
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A brief introduction of PMT‚ IPMT and PPMT Excel functions MS Excel – PMT Function(WS‚ VBA) • In Excel‚ the PMT function returns the payment amount for a loan based on an interest rate and a constant payment schedule. • The syntax for the PMT function is: • PMT( interest_rate‚ number_payments‚ PV‚ [FV]‚ [Type] ) • • • • interest_rate is the interest rate for the loan. number_payments is the number of payments for the loan. PV is the present value or principal of the loan
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HADNOUT E.13 - EXAMPLES ON TRANSFER FUNCTIONS‚ POLES AND ZEROS Example 1 Determine the transfer function of the mass-spring-damper system. The governing differential equation of a mass-spring-damper system is given by m x + c x + kx = F . Taking the Laplace transforms of the above equation (assuming zero initial conditions)‚ we have ms 2 X ( s ) + csX ( s ) + kX ( s ) = F ( s )‚ X ( s) 1 ⇒ = . 2 F ( s ) ms + cs + k Equation (1) represents the transfer function of the mass-spring-damper system. Example
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6-1 Inverse Trig Functions p. 468: 1-31 odd I. Inverse Trig Functions A. [pic] B. [pic] C. [pic] Find the exact value of each expression 1. [pic] 2. [pic] 3. [pic] 4. [pic] 5. [pic] 6. [pic] Use a calculator to find each value. 7. [pic] 8. [pic] 9. [pic] Find the exact value of each expression. 10. [pic] 11. [pic] 12. [pic] 6-2 Inverse Trig Functions Continued p. 474:1-41
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Student Activity A Generic Function Use the generic graph of f(x) with domain [–6‚ –3] and [–2‚ 6] to answer the questions below. 7 Y 6 5 4 3 2 1 X -7 -6 -5 -4 -3 -2 -1 0 -1 1 2 3 4 5 6 7 -2 -3 -4 -5 -6 -7 1. What is the range of f(x)? 2. What is the domain? 3. On what intervals is f(x) decreasing? 4. On what intervals will the following statements be true? a) As x increases‚ y increases. b) As x increases
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AP Calculus Name ____________________________ Period _____ Functions Defined by Integrals The graph below is‚ the derivative of. The graph consists of two semicircles and one line segment. Horizontal tangents are located at and and a vertical tangent is located at. 1. On what interval is increasing? Justify your answer. 2. For what values of x does have a relative minimum? Justify. 3. On what intervals is concave up? Justify 4. For what values of x is undefined? 5. Identify
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