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Survey of Mathematics with Applications, A, a la Carte edition plus NEW MyLab Math with Pearson eText (10th Edition)
10th Edition
ISBN: 9780134112237
Author: Allen R. Angel, Christine D. Abbott, Dennis Runde
Publisher: PEARSON
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Question
Chapter 7.2, Problem 54E
To determine
To find: The metric unit that would best express the volume of the statement “Air in a hot air balloon”.
Expert Solution & Answer
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Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
A
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3t)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot(3πt)
sin(3лt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411-
4
-2 sin (3лt)
(d)…
5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
Chapter 7 Solutions
Survey of Mathematics with Applications, A, a la Carte edition plus NEW MyLab Math with Pearson eText (10th Edition)
Ch. 7.1 - In Exercises 110, fill in the blanks with an...Ch. 7.1 - Prob. 2ECh. 7.1 - In Exercises 110, fill in the blanks with an...Ch. 7.1 - Prob. 4ECh. 7.1 - In Exercises 110, fill in the blanks with an...Ch. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - In Exercises 1116, match the given prefix with the...Ch. 7.1 - Complete the following. a. 1 hectogram = ________...Ch. 7.1 - Complete the following. a. 1 centiliter =...Ch. 7.1 - In Exercises 1923, without referring to any of the...Ch. 7.1 - Prob. 20ECh. 7.1 - In Exercises 1923, without referring to any of the...Ch. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Maximum Mass In Exercises 25 and 26, use the photo...Ch. 7.1 - Prob. 26ECh. 7.1 - In Exercises 2732, fill in the missing values. 27....Ch. 7.1 - Prob. 28ECh. 7.1 - In Exercises 2732, fill in the missing values. 29....Ch. 7.1 - Prob. 30ECh. 7.1 - In Exercises 2732, fill in the missing values. 31....Ch. 7.1 - In Exercises 2732, fill in the missing values. 32....Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3338, convert the given unit to the...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - Prob. 40ECh. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 3946, use the following information...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - In Exercises 4752, arrange the quantities in order...Ch. 7.1 - Walking Would you be walking faster if you walked...Ch. 7.1 - Who Ran Faster Jim ran 100 m, and Bob ran 100 yd...Ch. 7.1 - Water Removal One pump removes 1 da of water in 1...Ch. 7.1 - Balance If 5 kg ate placed on one side of a...Ch. 7.1 - Mount Fuji and Pikes Peak The most visited...Ch. 7.1 - 2014 Ford Mustang The 2014 Ford Mustang gets about...Ch. 7.1 - Calcium Tablets Sean lakes two 250-mg chewable...Ch. 7.1 - Framing a Painting A painting, including the...Ch. 7.1 - Liters of Soda A bottle of soda contains 360 m. a....Ch. 7.1 - Track and Field A high school has a 400-m oval...Ch. 7.1 - A Home Run A baseball diamond is a square whose...Ch. 7.1 - Prob. 64ECh. 7.1 - In Exercises 6568, fill in the blank to make a...Ch. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - Prob. 70ECh. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - In Exercises 110, fill in the blanks with an...Ch. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - Prob. 9ECh. 7.2 - Prob. 10ECh. 7.2 - In Exercises 1118, indicate the metric unit of...Ch. 7.2 - Prob. 12ECh. 7.2 - In Exercises 1118, indicate the metric unit of...Ch. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - Prob. 16ECh. 7.2 - In Exercises 1118, indicate the metric unit of...Ch. 7.2 - Prob. 18ECh. 7.2 - In Exercises 1924, choose the best answer. 19. The...Ch. 7.2 - In Exercises 1924, choose the best answer. 20. A...Ch. 7.2 - In Exercises 1924, choose the best answer. 21. The...Ch. 7.2 - Prob. 22ECh. 7.2 - In Exercises 1924, choose the best answer. 23. The...Ch. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - In Exercises 2530, (a) estimate the item in metric...Ch. 7.2 - Prob. 28ECh. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - In Exercises 3136, indicate the metric unit of...Ch. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - In Exercises 3742, choose the best answer. 37. A...Ch. 7.2 - In Exercises 3742, choose the best answer. 38. The...Ch. 7.2 - In Exercises 3742, choose the best answer 39. The...Ch. 7.2 - In Exercises 3742, choose the best answer. 40. The...Ch. 7.2 - In Exercises 3742, choose the best answer 41. The...Ch. 7.2 - In Exercises 3742, choose the best answer 42. The...Ch. 7.2 - Prob. 43ECh. 7.2 - In Exercises 4348, (a) estimate the area of the...Ch. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - In Exercises 4348, (a) estimate the area of the...Ch. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - In Exercises 4956, determine the metric unit that...Ch. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - In Exercises 4956, determine the metric unit that...Ch. 7.2 - In Exercises 4956, determine the metric unit that...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - In Exercises 5764, choose the best answer to...Ch. 7.2 - Prob. 64ECh. 7.2 - Prob. 65ECh. 7.2 - Prob. 66ECh. 7.2 - Prob. 67ECh. 7.2 - In Exercises 6568, (a) estimate the volume in...Ch. 7.2 - In Exercises 6972, select the best answer. 69. One...Ch. 7.2 - In Exercises 6972, select the best answer. 70. One...Ch. 7.2 - In Exercises 6972, select the best answer. 71. One...Ch. 7.2 - Prob. 72ECh. 7.2 - Prob. 75ECh. 7.2 - Prob. 76ECh. 7.2 - Prob. 77ECh. 7.2 - Prob. 78ECh. 7.2 - Prob. 79ECh. 7.2 - Prob. 80ECh. 7.2 - In Exercises 7386, when appropriate, use the key...Ch. 7.2 - Prob. 82ECh. 7.2 - Prob. 83ECh. 7.2 - Prob. 84ECh. 7.2 - Prob. 85ECh. 7.2 - Prob. 86ECh. 7.2 - Prob. 87ECh. 7.2 - Prob. 88ECh. 7.2 - Prob. 89ECh. 7.2 - Prob. 90ECh. 7.2 - Prob. 91ECh. 7.2 - Prob. 92ECh. 7.2 - In Exercises 9396, fill in the blank. 93. 501 cm3...Ch. 7.2 - In Exercises 9396, fill in the blank. 94. 435 cm3...Ch. 7.2 - In Exercises 9396, fill in the blank. 95. 263 k =...Ch. 7.2 - In Exercises 9396, fill in the blank. 96. 4.2 =...Ch. 7.2 - Glacier In Exercises 97 and 98, assume that a part...Ch. 7.2 - Glacier In Exercises 97 and 98, assume that a part...Ch. 7.2 - Challenge Problems/Group Activities In Exercises...Ch. 7.2 - Challenge Problems/Group Activities In Exercises...Ch. 7.2 - Prob. 101ECh. 7.2 - Prob. 102ECh. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 18, fill in the blanks with an...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 918, indicate the metric unit of...Ch. 7.3 - In Exercises 1924, select the best answer. 19. The...Ch. 7.3 - In Exercises 1924, select the best answer. 20. The...Ch. 7.3 - In Exercises 1924, select the best answer. 21. The...Ch. 7.3 - In Exercises 1924, select the best answer. 22. The...Ch. 7.3 - In Exercises 1924, select the best answer. 23. The...Ch. 7.3 - In Exercises 1924, select the best answer. 24. The...Ch. 7.3 - In Exercises 2528, estimate the mass of the item....Ch. 7.3 - In Exercises 2528, estimate the mass of the item....Ch. 7.3 - In Exercises 2528, estimate the mass of the item....Ch. 7.3 - In Exercises 2528, estimate the mass of the item....Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 2936, choose the best answer. Use...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - In Exercises 3750, convert each temperature as...Ch. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Curry As shown in the photo, curry being sold at...Ch. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Prob. 62ECh. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Prob. 66ECh. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Fish Tank A rectangular fish tank is 1 yd long by...Ch. 7.3 - Prob. 71ECh. 7.3 - Prob. 72ECh. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with aft...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 110, fill in the blanks with an...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 1126, convert the quantity to the...Ch. 7.4 - In Exercises 2730, use the part of the scorecard...Ch. 7.4 - In Exercises 2730, use the part of the scorecard...Ch. 7.4 - In Exercises 2730, use the part of the scorecard...Ch. 7.4 - In Exercises 2730, use the part of the scorecard...Ch. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 32ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 50ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - In Exercises 3159, when necessary round your...Ch. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 16, indicate the meaning of the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 712, change the given quantity to the...Ch. 7 - In Exercises 13 and 14, arrange the quantities...Ch. 7 - In Exercises 13 and 14, arrange the quantities...Ch. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - A square kilometer is a square with length and...Ch. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - Prob. 49RECh. 7 - Prob. 50RECh. 7 - Prob. 51RECh. 7 - Prob. 52RECh. 7 - Prob. 53RECh. 7 - Prob. 54RECh. 7 - Prob. 55RECh. 7 - Prob. 56RECh. 7 - Prob. 57RECh. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Prob. 3TCh. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - Prob. 10TCh. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - Prob. 13TCh. 7 - Prob. 14TCh. 7 - Prob. 15TCh. 7 - Prob. 16TCh. 7 - Prob. 17TCh. 7 - At the Aquarium A rectangular fish tank at an...Ch. 7 - Cost of Paint The first coat of paint for the...Ch. 7 - Prob. 20T
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- 1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forwardProblem 1.We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.(d) We assume that you sell the American put to a market participant A for the pricefound in (b). Explain how you act on the market…arrow_forward
- What is the standard scores associated to the left of z is 0.1446arrow_forward2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.015. Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ASK YOUR TEACHER 3 1 3 + dy, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule Need Help? Read It Watch Itarrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3πt) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot (3πt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1 (d) Express the slope of the rod…arrow_forward
- Consider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusionarrow_forwardNote: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…arrow_forward4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of aboutarrow_forward
- 6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4arrow_forwardThe general solution X'=Ax is given. Discuss the nature of the solutions in a neighborhood of (0,0) -2-2 (²) |a) A = (23) X(A) = (₁ (fi)e* + (2 (2) eht -2-5arrow_forwardshow work in paperarrow_forward
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