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Given 3 int values, a b c, print their sum. However, if any of the values is a teen - in the range 13..19 inclusive - then that value counts as 0, except 15 and 16 do not count as teens. You may write a separate helper function if you like. Define the helper above the problem function. input of 1, 2, 3 ā 6 input of 2, 13, 1 ā 3 input of 2, 1, 14 ā 3
Akash M.
Math 103: College Algebra 3.3 applications HW Directions: Complete all problems on separate paper. For each problem, you must find a function to maximize or minimize. For full credit, the function must be correct. Upload pictures or a scan of your solutions no later than Monday, October 19, 11:59 p.m. CST. 1. You have a 1200-foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What are the dimensions of the largest such enclosure? 2. Your factory produces lemon-scented air fresheners. You know each unit is cheaper, the more your produce. But you also know that costs will eventually go up if you make too many, due to storage of the overstock. The guy in accounting says that your cost for producing x thousand units a day can be approximated by the formula C(x)=0.04x^2-8.504x+25302. Find the daily production level that will minimize your costs. 3. Find a pair of numbers whose product is a maximum if twice the first number plus the second number is 48. 4. The sum of the length and width of a rectangle is 25 cm. Find the maximum area. 5. A piece of wire 20 feet long is cut into two pieces and each piece is bent to form a square. Determine the length of the two pieces so that the sum of the areas of the two squares is a minimum. 6. You run a canoe-rental business on a small river. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. Use this information to attempt to maximize your income. What should you charge? 7. The table lists the number of Americans (in thousands) who are expected to be over 100 years old for selected years. Year 1994 1996 1998 2000 2002 2004 Number (in thousands) 50 56 65 75 94 110 a. Find a quadratic function to fit the data set. Write it in proper form. b. How many Americans will be over 100 years old in the year 2008? c. In what year will the number of Americans over 100 years old exceed 200,000? 8. There is a sweet "shoot a pumpkin out of a cannon" contest held in the middle of nowhere. To be fair, pumpkins of nearly equal size are launched each time. The table shows the horizontal distance (in feet) said pumpkins travel when launched at different angles. Angle (in degrees) 20 30 40 50 60 70 Distance (in feet) 372 462 509 501 437 323 a. Explain why it's practical to use a quadratic function to model this data set (and the reason can't just be because the scatter plot looks like a parabola-think about why this scatter plot should look like it does!). b. Find a quadratic function to fit the data set. Write it in proper form. c. Use your model to determine at which angle the pumpkin should be launched in order for it to travel the farthest.
Sri K.
Objectives Familiarize the student with: - using the while loop; - converting verbally defined loops into actual Python code. Scenario In 1937, a German mathematician named Lothar Collatz formulated an intriguing hypothesis (it still remains unproven) which can be described in the following way: - take any non-negative and non-zero integer number and name it c0; - if it's even, evaluate a new c0 as c0 / 2; - otherwise, if it's odd, evaluate a new c0 as 3 * c0 + 1; - if c0 != 1, skip to point 2. The hypothesis says that regardless of the initial value of c0, it will always go to 1. Of course, it's an extremely complex task to use a computer in order to prove the hypothesis for any natural number (it may even require artificial intelligence), but you can use Python to check some individual numbers. Maybe you'll even find the one which would disprove the hypothesis. Write a program which reads one natural number and executes the above steps as long as c0 remains different from 1. We also want you to count the steps needed to achieve the goal. Your code should output all the intermediate values of c0, too. Hint: the most important part of the problem is how to transform Collatz's idea into a while loop - this is the key to success. Test your code using the data we've provided. Test Data Sample input: 15 Expected output: 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 steps = 17 Sample input: 16 Expected output: 8 4 2 1 steps = 4 Sample input: 1023 Expected output: 3070 1535 4606 2303 6910 3455 10366 5183 15550 7775 23326 11663 34990 17495 52486 26243 78730 39365 118096 59048 29524 14762 7381 22144 11072 5536 2768 1384 692 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 steps = 62
Supreeta N.
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