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please make sure u answer right and if u can write the formula for each qoustion it will be nice

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MAT-1221 Problem Set #2 Due 16 NOV 2018 Name: Instructions: • Remember that your work is graded holistically, based on the rubric below. • Show your work. Your work should include enough detail so that one can easily understand how to work out the problem and find the answer by reading your solution. • All matrix operations and inverse calculations should be done by hand; you may find it helpful to check your calculations on a calculator. • Academic Integrity: It is okay to work together on this, and to seek help from others, so long as the problem set that you turn in accurately reflects your understanding of the problems and their solutions. Mathematics Grading Rubric 5 (100%) 4 (87%) 3 (75%) 2 (60%) 1 (40%) or 0∗ (0%) Outstanding (“A”) Good (“B”) Average (“C”) Deficient (“D”) Failing (“F”) Well-executed, well-communicated, essentially correct Generally well- Adequately exe- Flawed execution Unsatisfactory executed but may cuted but with possibly with non- execution and/or have minor com- some non-trivial er- trivial errors or poor communication munication flaws or rors or inconsistent communication with fundamental some math errors communication errors *Note: A blank page, complete nonsense or a haphazard approach (one without a reasonable direction/order) will earn a zero. MAT-1221 Problem Set #2 This page intentionally left blank. Due 16 NOV 2018 MAT-1221 Problem Set #2 1 1) Find the domain of the function f (x) = √ . 5+x Due 16 NOV 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 2 2) Let f (x) = x + 2x, and evaluate the following expression. f (x + h) − f (x) Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #2 3) Describe the transformations to apply to the graph √ 3 below) to obtain the graph of f (x) = x (shown √ 3 of g(x) = 3 − x + 2. Then sketch the graph of g(x) on the axes provided. Due 16 NOV 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #2 4) Match each equation with the graph of one of the functions f , g, m, or n in the figure. There isn’t much work to show for this– you need only indicate your answers. You may indicate your reasons, if you wish (this could help earn more credit for a wrong answer). a) y = (x − 3)2 − 4 c) y = −(x − 3)2 + 4 b) y = −(x + 3)2 + 4 d) y = (x + 3)2 − 4 Due 16 NOV 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #2 Due 16 NOV 2018 5) Consider the quadratic equation 2x2 + 5x − 3 = 0. a) Solve by factoring. Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 b) Solve by completing the square. Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #2 6) Complete the square on the quadratic function f (x) = 0.5x2 + 4x + 5 to write it in vertex form. Then find each of the following. Due 16 NOV 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×2 a) vertex b) x- and y-intercepts c) maximum or minimum d) sketch a graph of the function (a set of axes is provided on the next page) MAT-1221 Problem Set #2 Due 16 NOV 2018 MAT-1221 Problem Set #2 7) Match each equation with the graph of f , g, h, or k in the figure. There isn’t much work to show for this– you need only indicate your answers. You may indicate your reasons, if you wish (this could help earn more credit for a wrong answer). x c) y = (0.5)x a) y = 14 b) y = 5x d) y = 3x Due 16 NOV 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #2 8) This exercise illustrates a situation in which the common log is particularly useful, where the natural log is not. In the scientific community, expressing very large or very small numbers is done using scientific notation. A number in scientific notation is written as Due 16 NOV 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×2 a × 10k where 1 ≤ a < 10, and k is an integer that corresponds to the magnitude of the number (the direction and number of spaces one needs to move the decimal place to end up with the number a, from the original number). Positive exponents correspond to large numbers, negative exponents correspond to small numbers (less than 1). For example: 2, 340, 000 = 2.34 × 106 , and 0.0000307 = 3.07 × 10−5 . Consider the (very large) number 7531 . If you wanted to get an expression of this number in decimal form, using scientific notation, you might first try plugging it into your calculator. On the TI-84, this results in an “overflow error”; the number is just too big for the calculator to handle. We can still accomplish our goal with the use of the common log! Start by letting N = 7531 , so that we want to write N in scientific notation, and take the common log of both sides. Now use properties of logs, along with the LOG function on the calculator to write N in scientific notation. MAT-1221 Problem Set #2 Due 16 NOV 2018 9) Suppose that you have $3000 that you can deposit into an account with a 4.2% annual interest rate. How long will it take for your account to reach $5000 if a) the account is compounded quarterly? Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 b) the account is compounded continuously? Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #2 10) An ordinary annuity pays 6.48% compounded monthly. A person wants to make equal monthly deposits into the account for 15 years in order to then make equal monthly withdrawals of $1,500 for the next 20 years, reducing the balance to zero. How much should be deposited each month for the first 15 years? What is the total interest earned during this 35-year process? Due 16 NOV 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×2
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