Numerade

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7. Let $p(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_0$. Task: • Describe an algorithm on "paper" using pseudocode, that you can employ the Horner's algorithm idea to efficiently calculate the Taylor polynomial (coefficients) of degree $m \le n$ of the given polynomial $p(x)$ centered around any point $x_0 \neq 0$. Specifically, you need to determine the coefficients $c_k = \frac{p^{(k)}(x_0)}{k!}$ for $k = 0, 1, ..., m$. (you may choose to follow the hint below) • Briefly explain why this algorithm will also work if $m < n$. • Write the Matlab code to efficiently implement this algorithm • Choose the polynomials from problem 3 and 4 and calculate the Taylor polynomial of the same degree centered at $x_0 = 1.73$ using your code. Verify your code by comparing the values of the original polynomial and its Taylor polynomial at several points. • Test also your code by computing the values at those same points as the previous bullet, of thes computed one-degree-less Taylor polynomials, around the same $x_0$. Hint: • Start by evaluating $p(x_0)$. What does it give you? • Conceptually subtract $p(x_0)$ from $p(x)$ to form a new polynomial, and recognize that it has $(x-x_0)$ as a factor. Use an idea similar to Horner's method to factor out $(x-x_0)$ iteratively, forming a polynomial $q(x)$ such that $(x-x_0)q(x) = p(x) - p(x_0)$. • Efficiently evaluate just the $q(x_0)$ what does it give you now? Repeat this process.

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12. If $ V_{1}=5 \mathrm{~V} $ in the circuit, find $ I_{5} $. A. $ 2 \mathrm{~mA} $ B. $ 3 \mathrm{~mA} $ C. $ 4 \mathrm{~mA} $ D. $ 5 \mathrm{~mA} $

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Part A If it requires energy $U$ to accelerate a rocket from rest to $\frac{1}{2}c$, the energy needed to accelerate that rocket from $\frac{1}{2}c$ to $c$ would be $\frac{1}{2}U$ $U$ $2U$ Infinite

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Which theory of deviance is the basis of the chapter "On Being Sane in Insane Places"? Labeling Critical Constructionism Social Learning Control

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Explain the process of speciation through an example. What starts the process of allopatric speciation? (include both genes and environment) Natural Selection Postulate 1: Competition in both populations Natural Selection Postulate 2: Variation & Differential Reproductive Success in both populations Natural Selection Postulate 3: Inheritance Natural Selection Results (Generation 1) Speciation Results (Generation 20) Speciation Results (Generation 200)

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Under certain water conditions, the free chlorine (hypochlorous acid, HOCI) in a swimming pool decomposes according to the law of uninhibited decay. After shocking a pool, the pool boy, Geoff, tested the water and found the amount of free chlorine to be 2.3 parts per million (ppm). Twenty-four hours later, Geoff tested the water again and found the amount of free chlorine to be 1.9 ppm What will be the reading after 3 days (that is, 72 hours)? When the chlorine level reaches 1.0 ppm, Geoff must shock the pool again. How long can Geoff go before he must shock the pool again? After 3 days, or 72 hours, the amount of free chlorine in the pool will be ppm. (Do not round until the final answer. Then round to the nearest hundredth as needed.) Geoff will need to shock the pool again in hours (Do not round until the final answer. Then round to the nearest tenth as needed)

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FXERCISE 1. Write a short note on history and evaluation of HTML. 2. Explain structure of HTML document by giving a simple example of an HTML document. 3. What is an HTML element? Give structure of an HTML element. 4. How ro view an HTML document on your desktop? 5. List any three browsers. 6. Explain various HTML heading styles by giving examples, 7. Explain various HTML formatting lags by giving examples. 8. Explain preformatted text in HTML by giving an example. 9. Write a short note on anchor tag of HTML. 10. Define and explain absolute and relative address in HTML.

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3. Parameterize the plane through the points (1, 2, 3), (2, 5, 8), and (5, 2, 0). 4. Give two nonparallel vectors and the coordinates of a point in the plane with parametric equations x = 2s + 3t, y = s - 5t, z = -s + 2t.

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If the central bank wants to increase the money supply, it can A. increase the discount rate. B. sell bonds in the market for bonds. C. buy bonds in the market for bonds. D. increase the reserve requirement for banks. The Federal Reserve can A. not determine the federal funds rate because it is determined in the private sector. B. determine the federal funds rate by changing the supply of central bank money. C. determine the discount rate by changing the supply of central bank money. D. only control the money supply; it cannot determine the interest rate.

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6. [-/1 Points] DETAILS MY NOTES Math 110 Course Resources Applications of Definite Integrals Course Packet on income streams and annuities A math tee shirt business is expected to generate $20,000 in revenue per year for the next 5 years. If the income is reinvested in the business at a rate of 5% per year compounded continuously, determine the future value of this income stream at the end of 5 years. Future value (exact value) = ____ dollars Future value (rounded to the nearest cent) = ____ dollars 7. [-/1 Points] DETAILS MY NOTES Math 110 Course Resources Applications of Definite Integrals Course Packet on income streams and annuities A math tee shirt business is expected to generate $15,000 in revenue per year for the next 20 years. If the income is reinvested in the business at a rate of 2% per year compounded continuously, determine the present value of this income stream. Present value (exact value) = ____ dollars Present value (rounded to the nearest cent) = ____ dollars 8. [-/1 Points] DETAILS MY NOTES

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