
Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Question
Chapter 8.3, Problem 5EE
To determine
(a)
Three different elements of the group derived from translations.
To determine
(b)
Two different centre points about which a 180
To determine
(c)
Two different centre points about which a 120
To determine
(d)
Three distinct lines that could serve as axis of reflection for elements of the group.
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The purpose of this problem is to solve the Black-Scholes PDE with analytical techniques,
which will lead us back to the Black-Scholes formula. The technique is very similar to the
one used with the Feynman-Kac formula back in MATH 467.
Let's consider the PDE given by
with terminal condition f(T,x)
af
+
Ət
1
02
ર
.2მ2 f
af
მ2
+rx
მე
- rf = 0,
=
(x-K)+. The solution f(t, x) corresponds to the price
of a call option (given the initial condition) at time t if the stock price is x.
(a) The first two things that prevent us from solving this PDE directly are
(i) the fact that we have a terminal condition, instead of an initial condition;
(ii) the terms in front of the derivatives are not constant.
To address these, we use the transformation g(t, x) = ƒ(T − t,e³), equivalent to
f(t, x) = g(T-t, log(x)). Under this condition, determine the PDE and the initial
condition satisfied by g.
(b) Now, the PDE obtained in (a) should have an initial condition and constant coeffi-
cients, but it still…
٣:٥٣
النموذج الاول
. . .
O O O
بشما ند الحمر الحمر
الجمهورية الجنية
وزارة التربية والتعليم
اليوم
التاريخ
اللجنة العليا للاختبارات
الزمن
اختبار مادة الجبر والهندسة
لجنة المطابع السرية المركزية
للشهادة الثانوية العامة (القسم العلمي)
الفترة
%97
(1)
ظلل في ورقة الإجابة الدائرة التي تحتوي على الحرف ( ص ) للإجابة الصحيحة والحرف ( خ ) للإجابة الخطأ بحسب رقم الفقرة لكل مما يأتي ( درجة لكل فقرة )
)1
)
2
)
3
)
4
) بؤرة القطع س" = ١٢ ص هي (
۲
) طول المحور الأصغر للقطع ٩ س + ص = ٩ يساوي 6 وحدات طول .
) إذا كان & عدد مركب ، 181 + 11 = ٦ ، فإن ١١ = ٣ .
) إذا كان م + ۳ ت = ۲ + ت ب م ، ب دع ، فإن م + ب =
5 ( ) إذا كان & = ۱ + ٣ ت ، فإن ٠ = ١٠ .
6 ( - ) إذا كان ٥٠ - ٣ - ١٢٠ ٤ - ٣ ، فإن قيمة ٧ = ٥ .
1
)
=
N
) إذا كان ح هو الحد الخالي من س في المفكوك ( س +
v. N
8 ( ( قيمة المقدار , = + ۱ ، * . . +
، فإن قيمة ٧ = ١٦ .
۱ +
9 ( ) المستقيمان المقاربان للقطع الذي معادلته س" = ١ هما ص = :
۹
10 ( ) إذا كان ٥ + س = ٢٤ ، فإن قيمة س = - 1
س
11 ( ) إذا كانت النسبة بين الحدين الأوسطين تساوي 9 في المفكوك ( س + - ) ،…
Chapter 8 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 8.1 - Determine the day of the week on which you were...Ch. 8.1 - Determine the day of the week on which Abraham...Ch. 8.1 - Determine the day of the week on which January 1,...Ch. 8.1 - Determine the day of the week on which Valentines...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 4ESCh. 8.1 - Prob. 5ESCh. 8.1 - Prob. 6ES
Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 8ESCh. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 10ESCh. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 14ESCh. 8.1 - Evaluate each expression, where and indicate...Ch. 8.1 - Prob. 16ESCh. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Prob. 22ESCh. 8.1 - Prob. 23ESCh. 8.1 - Military Time. Evaluate each expression, where +...Ch. 8.1 - Evaluate each expression, where + and indicate...Ch. 8.1 - Prob. 26ESCh. 8.1 - Evaluate each expression, where + and indicate...Ch. 8.1 - Prob. 28ESCh. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Prob. 32ESCh. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Determine whether the congruence is true or false....Ch. 8.1 - Prob. 38ESCh. 8.1 - List five different natural numbers that are...Ch. 8.1 - List five different natural numbers that are...Ch. 8.1 - Perform the modular arithmetic. (9+15)mod7Ch. 8.1 - Prob. 42ESCh. 8.1 - Perform the modular arithmetic. (5+22)mod8Ch. 8.1 - Prob. 44ESCh. 8.1 - Perform the modular arithmetic. (42+35)mod3Ch. 8.1 - Prob. 46ESCh. 8.1 - Perform the modular arithmetic. (37+45)mod12Ch. 8.1 - Prob. 48ESCh. 8.1 - Prob. 49ESCh. 8.1 - Perform the modular arithmetic. (2510)mod4Ch. 8.1 - Prob. 51ESCh. 8.1 - Prob. 52ESCh. 8.1 - Prob. 53ESCh. 8.1 - Prob. 54ESCh. 8.1 - Perform the modular arithmetic. (1532)mod7Ch. 8.1 - Prob. 56ESCh. 8.1 - Perform the modular arithmetic. (68)mod9Ch. 8.1 - Prob. 58ESCh. 8.1 - Prob. 59ESCh. 8.1 - Prob. 60ESCh. 8.1 - Perform the modular arithmetic. (1418)mod5Ch. 8.1 - Prob. 62ESCh. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Prob. 66ESCh. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Clocks and Calendars. Use modular arithmetic to...Ch. 8.1 - Prob. 71ESCh. 8.1 - Prob. 72ESCh. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Prob. 75ESCh. 8.1 - Prob. 76ESCh. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Prob. 79ESCh. 8.1 - Prob. 80ESCh. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Find all whole number solutions of the congruence...Ch. 8.1 - Prob. 83ESCh. 8.1 - Find the additive inverse and the multiplicative...Ch. 8.1 - Find the additive inverse and the multiplicative...Ch. 8.1 - Prob. 86ESCh. 8.1 - Find the additive inverse and the multiplicative...Ch. 8.1 - Find the additive inverse and the multiplicative...Ch. 8.1 - Modular division can be performed by considering...Ch. 8.1 - Prob. 90ESCh. 8.1 - Prob. 91ESCh. 8.1 - Prob. 92ESCh. 8.1 - Prob. 93ESCh. 8.1 - Modular division can be performed by considering...Ch. 8.1 - Prob. 95ESCh. 8.1 - Prob. 96ESCh. 8.1 - Prob. 97ESCh. 8.1 - Prob. 98ESCh. 8.1 - Prob. 99ESCh. 8.1 - Many people consider the 13th of the month an...Ch. 8.2 - What is the ciphertext for the word CODE?Ch. 8.2 - Prob. 2EECh. 8.2 - Prob. 3EECh. 8.2 - Prob. 4EECh. 8.2 - Prob. 5EECh. 8.2 - ISBN Numbers. Determine whether the given number...Ch. 8.2 - ISBN Numbers. Determine whether the given number...Ch. 8.2 - Prob. 3ESCh. 8.2 - Prob. 4ESCh. 8.2 - Prob. 5ESCh. 8.2 - ISBN Numbers. Determine whether the given number...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - Prob. 10ESCh. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - ISBN Numbers. Determine the correct check digit...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - UPC Codes. Determine the correct check digit for...Ch. 8.2 - Prob. 23ESCh. 8.2 - Prob. 24ESCh. 8.2 - Money Orders Some money orders have serial numbers...Ch. 8.2 - Money Orders Some money orders have serial numbers...Ch. 8.2 - Air Travel Many printed airline tickets contain a...Ch. 8.2 - Air Travel Many printed airline tickets contain a...Ch. 8.2 - Air Travel Many printed airline tickets contain a...Ch. 8.2 - Prob. 30ESCh. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Prob. 33ESCh. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Prob. 35ESCh. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Credit Card Numbers. Determine whether the given...Ch. 8.2 - Prob. 38ESCh. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Encryption. Encode the message by using a cyclical...Ch. 8.2 - Decoding. Use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding. Use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding. Use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding. Use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding, use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding, use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding, use a cyclical alphabetic encrypting...Ch. 8.2 - Decoding, use a cyclical alphabetic encrypting...Ch. 8.2 - Encryption Julius Caesar supposedly used an...Ch. 8.2 - Decoding Julius Caesar supposedly used an...Ch. 8.2 - Encryption Use the encrypting congruence...Ch. 8.2 - Encryption Use the encrypting congruence...Ch. 8.2 - Encryption Use the encrypting congruence...Ch. 8.2 - Encryption Use the encrypting congruence...Ch. 8.2 - Decoding Decode the message LOFT JGMK LBS MNWMK...Ch. 8.2 - Decoding Decode the message BTYW SCRBKN UCYN that...Ch. 8.2 - Prob. 61ESCh. 8.2 - Decoding Decode the message GBBZ OJQBWJ TBR GJHI...Ch. 8.2 - Money Orders Explain why the method used to...Ch. 8.2 - Prob. 64ESCh. 8.2 - Banking. When banks process an electronic funds...Ch. 8.3 - Prob. 1EECh. 8.3 - Prob. 2EECh. 8.3 - Prob. 3EECh. 8.3 - Prob. 4EECh. 8.3 - Prob. 5EECh. 8.3 - Prob. 1ESCh. 8.3 - Prob. 2ESCh. 8.3 - Prob. 3ESCh. 8.3 - Prob. 4ESCh. 8.3 - Prob. 5ESCh. 8.3 - Prob. 6ESCh. 8.3 - Prob. 7ESCh. 8.3 - Prob. 8ESCh. 8.3 - Prob. 9ESCh. 8.3 - Prob. 10ESCh. 8.3 - Prob. 11ESCh. 8.3 - Prob. 12ESCh. 8.3 - Prob. 13ESCh. 8.3 - Prob. 14ESCh. 8.3 - Prob. 15ESCh. 8.3 - Prob. 16ESCh. 8.3 - Prob. 17ESCh. 8.3 - Prob. 18ESCh. 8.3 - Prob. 19ESCh. 8.3 - Prob. 20ESCh. 8.3 - Prob. 21ESCh. 8.3 - Prob. 22ESCh. 8.3 - Prob. 23ESCh. 8.3 - Prob. 24ESCh. 8.3 - Prob. 25ESCh. 8.3 - Prob. 26ESCh. 8.3 - Prob. 27ESCh. 8.3 - Prob. 28ESCh. 8.3 - Prob. 29ESCh. 8.3 - Prob. 30ESCh. 8.3 - Prob. 31ESCh. 8.3 - Prob. 32ESCh. 8.3 - Prob. 33ESCh. 8.3 - Prob. 34ESCh. 8.3 - Refer to the group of permutations of the numbers...Ch. 8.3 - Prob. 36ESCh. 8.3 - Prob. 37ESCh. 8.3 - Prob. 38ESCh. 8.3 - Prob. 39ESCh. 8.3 - Prob. 40ESCh. 8.3 - Prob. 41ESCh. 8.3 - Prob. 42ESCh. 8.3 - Prob. 43ESCh. 8.3 - Prob. 44ESCh. 8.3 - Prob. 45ESCh. 8.3 - Prob. 46ESCh. 8.3 - Prob. 47ESCh. 8.3 - Prob. 48ESCh. 8.3 - Prob. 49ESCh. 8.3 - Prob. 50ESCh. 8.3 - Prob. 51ESCh. 8.3 - Prob. 52ESCh. 8.3 - Prob. 53ESCh. 8.3 - Prob. 54ESCh. 8.3 - Prob. 55ESCh. 8.3 - Consider the set of elements a,b,c,d with the...Ch. 8.3 - Prob. 57ESCh. 8.3 - Prob. 58ESCh. 8.3 - Prob. 59ESCh. 8.3 - Prob. 60ESCh. 8.3 - Prob. 61ESCh. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression, where and indicate...Ch. 8 - Evaluate each expression. Where + and indicate...Ch. 8 - Evaluate each expression. Where + and indicate...Ch. 8 - Prob. 11RECh. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Clocks and Calendars. Use modular arithmetic to...Ch. 8 - Prob. 24RECh. 8 - Prob. 25RECh. 8 - Find all whole number solutions of the congruence...Ch. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - ISBN Numbers. Determine the correct check digit...Ch. 8 - ISBN Numbers. Determine the correct check digit...Ch. 8 - UPC Codes. Determine the correct check digit for...Ch. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Encryption. Encode the message using a cyclical...Ch. 8 - Encryption. Encode the message using a cyclical...Ch. 8 - Encryption. Use a cyclical alphabetic encrypting...Ch. 8 - Prob. 44RECh. 8 - Encryption Use the encrypting congruence...Ch. 8 - Encryption Decode the message WEU LKGGMF NHM NMGN,...Ch. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Prob. 53RECh. 8 - Use symbolic notation, shown below, for the...Ch. 8 - Prob. 55RECh. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Evaluate each expression, where and indicate...Ch. 8 - January 1, 2017, was a Sunday. What day of the...Ch. 8 - Determine whether the congruence is true or false....Ch. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 6TCh. 8 - Scheduling Disregarding A.M. or P.M., if it is now...Ch. 8 - Prob. 8TCh. 8 - Prob. 9TCh. 8 - Find the additive inverse and the multiplicative...Ch. 8 - ISBN Number Determine the correct check digit for...Ch. 8 - UPC Codes Determine the correct check digit for...Ch. 8 - Prob. 13TCh. 8 - Encryption Encrypt the plaintext message REPORT...Ch. 8 - Prob. 15TCh. 8 - Prob. 16TCh. 8 - Prob. 17TCh. 8 - Prob. 18TCh. 8 - In the permutation group of the numbers 1 2 3,...Ch. 8 - Prob. 20T
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- الاسم يمنع استخدام الآلة الحاسبة ظلل في ورقة الإجابة الدائرة التي تحتوي على الحرف (ص) للإجابة الصحيحة والحرف (خ) للإجابة الخطأ بحسب رقم الفقرة لكل مما يأتي: درجة لكل فقرة. ( ) نها جا 元 جتا = صفر س ۱ س س -۱ ( ) يمكن إعادة تعريف الدالة د(س) = س قاس لكي تكون متصلة عند س = 7 ( ) إذا كانت د(س) = (٢) س - س ) ؛ فإن د(١) = ٦ ٢ س ص ( ) إذا كانت س + 0= ؛ فإن عند ) - ١ ، - ٦ ) تساوي (٦) ( ) إذا كانت د(س) = س ه ، و (س) = ٣ س ٢ + ٢ س ؛ فإن ( د ) (۱) = ۸ ) ( معادلة ناظم الدالة ص = د(س) عند النقطة ) ( ، د (۲)) هي ص - (د (م) - - د (۲) ( س - م ) ( ) إذا كانت ص = ظتا٢ س ؛ فإن ص = ٢ ص قتا ٢س ) ( إذا كانت د(س) = س ؛ فإن د (T) = جتاس 1- T ( ) إذا كانت د(س) = 1 - جناس جاس ؛ فإن د () = - 1 ( ) إذا كانت الدالة د (س) تحقق شروط مبرهنة القيمة المتوسطة على [ ، ب ] ، فإنه يوجد جـ ] ، ب [ بحيث (جـ) = (P) + (~)- - ب + P 1 2 3 4 5 6 7 8 9 10 11 ( ) للدالة د(س) = لو ( س ) + (٣) نقطة حرجة عند س = . ( ) إذا كان س = - ٢ مقارباً رأسياً للدالة د(س) 12 10 13 14 15 16 17 س = لو|س | + ث - = ۲ س + ٣ ب س + ٤ ، فإن معادلة…arrow_forwardPlease help me answer question b and c for this problem.A student project involved collecting data to see if there was a difference in the amount of time one had to wait at the drive-thru between two fast food restaurants, A and B. She randomly selected 30 cars at fast food restaurant A and 30 cars at fast food restaurant B. For each car chosen, she recorded how much time passed from the placement of the order to receiving their food at the pick-up window. The data is given in the table below measured in Seconds. Use α=0.05.CSV…arrow_forwardPlease help me with the following statistics problem A long-distance runner wants to compare the durability of two running shoe brands: Brand A and Brand B. Instead of testing them separately, 15 runners simultaneously wear Brand A on the left foot and Brand B on the right foot during training runs. The runner continues training as usual and tracks how many kilometers each shoe lasts before showing significant wear (e.g., loss of cushioning, outsole damage). Since both shoes experience the same runner, terrain, and conditions, any lifespan difference can be attributed to the shoe brand rather than external factors. Test whether Brand A running shoes have a significantly shorter lifespan than Brand B when worn under the same conditions by the same runner. CSV: "","A","B" "A",197,193 "B",230,229 "C",179,180 "D",206,205 "E",182,180 "F",141,142 "G",207,207 "H",116,112 "I",78,79 "J",0,0 "K",213,212 "L",86,83 "M",181,181 "N",85,79 "O",73,71 The…arrow_forward
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