Find the equation of the tangent line to the circle (x+2)² +y+5)² =4 at point (-4,-5) (

1. Use the ę notation to prove the following limits:

lim n→∞ [n^2+ 3ncos(2n+1)+2] / [n^2−nsin(4n+3)+4] = 1

2. Let {an} a sequence converging to L > 0. Show ∃N ∈ N, ∀n ∈ N, n ≥ N, an > 0

3.Let {an} a sequence converging to L. Let {bn} a sequence such that ∃Nb ∈ N, ∀n ∈ N, n ≥ Nb, an = bn. Show that {bn} converges to L as well.

Thank you. Please complete proofs fully.

Consider the following page reference string: 0, 1, 2, 3, 1, 0, 4, 5, 1, 0, 1, 2, 6, 5, 2, 1, 0, 1, 2, 5 How many page faults would occur for the following replacement algorithms, assuming one, three, five, and seven frames? Remember that all frames are initially empty, so your first unique pages will cost one fault each. Optimal replacement LRU replacement CLOCK replacement FIFO replacement

1. Box #1 contains 4 red chips and 1 white chip. Box #2 contains 3 red, 1 black and 6 white chips. The experiment consists of randomly picking a box, then randomly picking a chip from it. Find the probability that: (a) A red chip is drawn from Box #1: ___________________________________ (b) A red chip is drawn, given that Box #1 was picked: ________________________________ (c) Box #1 was picked, given that the chip is black: _____________________________

Consider the following page reference string:

0, 1, 2, 3, 1, 0, 4, 5, 1, 0, 1, 2, 6, 5, 2, 1, 0, 1, 2, 5

How many page faults would occur for the following replacement algorithms, assuming one, three, five, and seven frames? Remember that all frames are initially empty, so your first unique pages will cost one fault each.

• Optimal replacement
• LRU replacement
• CLOCK replacement
• FIFO replacement

Design a 4-to-16-line decoder by using the minimum number of 2-to-4-line decoders. The 2-
to-4-line decoders have an enable input (‘1’=enabled) and the designed 4-to-16-line decoder
does not have an enable. Name the inputs A0...A3 and the outputs D0...D15.

Question from chapter 2 -3rtDa

In 2006 the State of Indiana in the USA sold a 75-year concession to operate and maintain the East-West Toll Road. Before doing so, it commissioned a consulting report that estimated the value of the concession.

Q: Calculate the present value of the concession using a discount rate of 6%. Cash flows are reported in Table 1 for each ten-year block up until 2066–2075 with the last block as five years (2076–2081). Assume in your calculations that cash flows are spread evenly during those blocks.

Find the general solution for differential equation

x^3y'''-(3x^2)y''+6xy'-6y=0, y(1)=2, y'(1)=1, y''(1)=-4  

4) Consider ? ⊆ ℝ × ℝ with {(?,?)|?² = ?²}. Prove that ? is an equivalence relation, and concisely characterize how its equivalence classes are different from simple real-number equality.

Problem 4-53 Special Orders (LO 4-1, 2)

Sherene Nili manages a company that produces wedding gowns. She produces both a custom product that is made to order and a standard product that is sold in bridal salons. Her accountant prepared the following forecasted income statement for March, which is a busy month:

Ms. Nili already has orders for the 10 custom dresses reflected in the March forecasted income statement. The depreciation charges are for machines used in the respective product lines. Machines depreciate at the rate of $1 per hour based on hours used, so these are variable costs. In March, cutting and sewing machines are expected to operate for 780 hours, of which 540 hours will be used to make custom dresses. The rent is for the building space, which has been leased for several years at $5,800 per month. The rent, heat, and light are allocated to the product lines based on the amount of floor space occupied.

A valued customer, who is a wedding consultant, has asked Ms. Nili for a special favor. This customer has a client who wants to get married in early April. Ms. Nili's company is working at capacity and would have to give up some other business to make this dress. She can't renege on custom orders already agreed to, but she can reduce the number of standard dresses produced in March to 10. Ms. Nili would lose permanently the opportunity to make up the lost production of standard dresses because she has no unused capacity for the foreseeable future. The customer is willing to pay $22,600 for the special order. Materials and labor for the order will cost $5,400 and $9,400, respectively. The special order would require 110 hours of machine time. Ms. Nili's company would save 120 hours of machine time from the standard dress business given up. Rent, heat and light, and other production costs would not be affected by the special order.

Required:

a-1. Calculate the differential operating profit (loss). (Select option "increase" or "decrease", keeping Without special order as the base. Select "none" if there is no effect.)

a-2. From an operating profit (loss) perspective for March, should Ms. Nili accept the order?

b. What is the minimum price Ms. Nili should accept to take the special order?