Concept explainers
Exercises 1-2 involve credit cards that calculate interest using the average daily balance method. The monthly interest rate is 1.5% of the average daily balance. Each exercise shows transactions that occurred during the march 1- march 31 billing period. In each exercise,
a. Find the average daily balance for the billing period. Round to the nearest cent.
b. Find the interest to be paid on April 1, the next billing date. Round to the nearest cent.
c. Find the balance due on April 1.
d. This credit card requires a $10 minimum monthly payment if the balance due at the end of the billing period is less than $360. Otherwise, the minimum monthly payment is $$ of the balance due at the end of the billing period, rounded up to the nearest whole dollar. What is the minimum monthly payment due by april9?
Transaction Description | Transaction Amount |
Previous balance, $7150.00 | |
March 1Billing date | |
March 4 Payment | $ 400 credit |
March 6 Charge: Furniture | $ 1200 |
March 15 Charge: Gas | $40 |
March 30 Charge: Groceries | $50 |
March 31 End of billing period | |
Payment Due Date: April 9 |
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Thinking Mathematically (6th Edition)
- 3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M a simple module? (b) State and prove Schur's Lemma for simple modules. (c) Let AM(K) and M = K" the natural A-module. (i) Show that M is a simple K-module. (ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a is a matrix in the centre of M, (K). [Recall that the centre, Z(M,(K)) == {a Mn(K) | ab M,,(K)}.] = ba for all bЄ (iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~ K as K-algebras. Is this consistent with Schur's lemma?arrow_forward(a) State, without proof, Cauchy's theorem, Cauchy's integral formula and Cauchy's integral formula for derivatives. Your answer should include all the conditions required for the results to hold. (8 marks) (b) Let U{z EC: |z| -1}. Let 12 be the triangular contour with vertices at 0, 2-2 and 2+2i, parametrized in the anticlockwise direction. Calculate dz. You must check the conditions of any results you use. (d) Let U C. Calculate Liz-1ym dz, (z - 1) 10 (5 marks) where 2 is the same as the previous part. You must check the conditions of any results you use. (4 marks)arrow_forward(a) Suppose a function f: C→C has an isolated singularity at wЄ C. State what it means for this singularity to be a pole of order k. (2 marks) (b) Let f have a pole of order k at wЄ C. Prove that the residue of f at w is given by 1 res (f, w): = Z dk (k-1)! >wdzk−1 lim - [(z — w)* f(z)] . (5 marks) (c) Using the previous part, find the singularity of the function 9(z) = COS(πZ) e² (z - 1)²' classify it and calculate its residue. (5 marks) (d) Let g(x)=sin(211). Find the residue of g at z = 1. (3 marks) (e) Classify the singularity of cot(z) h(z) = Z at the origin. (5 marks)arrow_forward
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