Solve y'(0)=Ay y(0) =v A=(7,-5;10,-8) v=(2;3)

KL Islamic Bank entered a two-year Istisna' contract to construct a power generator for a total price of $600.00 commencing 1 January 2007. The following costs were estimated at the time of concluding the contract.

                     31 December 2007             31 December 2008 Total

Materials                 120,000                                   60,000                               180,000

Wages                   180,000                                  120,000                               300,000

Total                        300,000                                  180,000                               480,000

Billings were made in year for 2008 for $225,000 and the remaining balance was billed at the end of year 2008.

Following is the payment schedule that was agreed with the client of KL Islamic Bank:

Year       % of total price

2007       25%

2008       30%

2009       45%

There was a substantial increase in material cost in 2008 due to the liquidation of a major supplier for the said material. Accordingly, the bank revised its cost estimate for material to be $60,000 higher than previously planned.

The bank recognizes revenue based on the percentage of completion method.

Required:

a. prepare all necessary journal entries for the year 2007 to 2009 to record the above transactions in the books of KL Islamic Bank.

b. prepare the Statement of Financial Position (extract) and Income Statements (extract) for the year 2007 and 2008 to present tne transactions relating to the contract.

Answer true or false for each statement and give a logically valid explanation to support your answer (you can give a counterexample if it is false, or make a proof if it is true).

a. The multiplication of two irrational numbers is an irrational number.

b. The set {( 1−n/ n , 8n+1/ n ) |n ∈ N } is an open covering of (−1, 8].

c. The sequence {( 1−3n /n + (−1)ⁿ ) |n ∈ N } has a sub-sequence that converges to -4.

d. The sum of the Lebesgue measure of the sets A = C ∪ [−5, 1), and B = Q ∩ [4, 10] is 6, where C is the Cantor ternary set, and Q is the rational numbers set.

e. Find the inf and sup of the set A = {x ∈ R : x ² − 4x ≤ 20 − 5x} are -5 and 4 respectively.

f. The intersection set for the following collection of intervals is open. {(−1/n − 2, 3 + 1/n), n ∈ N} .

A tree is called central if its center is K₁ and bicentral if its center is K₂. Show that every tree is either central or bicentral without using the theorem that the center of every connected graph G lies in a single block.

Recall that a set B is dense in R if an element of B can be found between any two real numbers a < b. Take p∈Z and q∈N in every case. It is given that the set of all rational numbers p/q with 10|p| ≥ q is not dense in R. Explain, using plain words (without a rigorous proof), why this is. That is, present a general argument in plain words. Does this set violate the Archimedean Property? If so, how? (PLEASE DON'T REPEAT THE ANSWERS TO THIS QUESTION ALREADY POSTED ON CHEGG)

On March 11, 2011, Japan suffered an earthquake and tsunami that caused a disastrous accident at the Fukushima nuclear power plant. Among many other results, amounts of iodine-131 that were 27 times the government limit were found in a sample of spinach 60 miles away.† Now, 27 times the government limit of iodine-131 is 54 thousand becquerels per kilogram.† The following table shows the amount I, in thousands of becquerels per kilogram, of iodine-131 that would remain after t days.

(a)

Show that the data are exponential. (In this part and the next, round to three decimal places.)

Because t increases by 1 each time, to show that the data are exponential, we must show that the successive ratios (rounded to three decimal places) are the same. Because all of the ratios are equal to  , the data are exponential.

(b)

Find an exponential model I that shows the amount of iodine-131 present after t days.

I(t) =

(c)

How long will it take for the amount of iodine-131 to fall to the government limit of 2 thousand becquerels per kilogram? Round your answer to the nearest whole day.

days

Verify the divergence theorem for the vector field F = 2xzi + yzj +z2k and V is the volume enclosed by the upper hemisphere x2 + y2 + z2 = a2, z ≥ 0

1. Solve for the optimal values of C1 and C2 in the following optimization problem: MaxC1,C2 C₁^1/2 + βC₂^1/2

s.t. C₁ + C₂ /1 + r = Y₁ + Y₂/1 + r

Hint: ∂C^1/2 /∂C = 1/2C^−1/2

When r goes up, how does C1 change? Does it increase or decrease?

Consider a region R bounded by the y-axis, the line segment y=8-x for x from 0 to 8, and part of the circle y=-sqrt(64-x^2) for x from 0 to 8. Find the centroid.

use well ordering principle to prove that sqrt(6) is not rational

A furniture company produces tables (X) and chairs (Y). Available resources have indicated that the production volume level should not exceed 1200 units per week and the demand for chairs is at most half of that for tables. Further, the production level of tables can exceed three times the production of chairs by at most 600 units. If the company makes a profit of OMR12 and OMR 16 per unit respectively on tables and chairs, how many of each should be produced weekly in order to maximize the profit. which of the following represents one of the constraints for the above business problem

Show that {xx^R | x,y ∈ {0,1}*} is a context-free language.

Note that x^R is the reversal of x.

Show all work.

Question is for Discrete Math Structures

Consider the nonhomogeneous equation y"-8y'+16y=e^4x cos x. Find a particular solution of the equation by the method undetermined coefficients.