You are the finance manager of your company. Your company is planning for capacity expansion and need to borrow RM850,000 from a local bank. The offered term loan will be amortised in 9 years with a nominal interest rate of 7.2% p.a. compounded monthly. The final payment will be at the end of Year 9.

1.Based on your working on an amortisation table, how much principal and interest would have your company paid after the first four months of payments?

2.If you have a choice, would you prefer to repay the above loan monthly (assume7.2% per year is compounded monthly) or annually (assume 7.2% per year is compounded annually) based on the total interest incurred? What is the main factor that contribute to such a difference in interest?

Let u = f(x,y), where x = rcosθ and y = rsinθ. Using the chain rules, carefully calculate the partial derivatives ∂u/ ∂r and ∂u/ ∂θ , and the second partial derivatives ∂2u/ ∂r2 and ∂2u/ ∂θ2 , in terms of r, θ, and the partial derivatives fx, fy, fxx, fxy, fyy.

∂u /∂r =

∂u /∂θ =

∂^2u/ ∂r^2 =

∂^2u ∂θ^2=

How many bit strings of length fifteen

a) Contain at least four 0s?

b) Contain at most four 0s?

c) Contain exactly four 0s?

d) Begin with four 0s?

Using Runge-Kutta method, compute y(0.3), from the equation dy dx = xy 1+x2 with y(0) = 1, take h = 0.1

If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 4 lbin is suddenly set in motion at t=0 by an external force of 63cos(12t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet.

Take the smallest cellular structure forthe circle X = S1 consisting
of a single 0-cell and a single 1-cell. Let Y be the same circle with two 0-cells and two
1-cells with the ends attached to the two different 0-cells. Count (in particular, describe)
all possible (up to homotopy) cellular maps X → Y and Y → X

question related to Topological data analysis 2

Take the smallest cellular structure forthe circle X = S1 consisting
of a single 0-cell and a single 1-cell. Let Y be the same circle with two 0-cells and two
1-cells with the ends attached to the two different 0-cells. Count (in particular, describe)
all possible (up to homotopy) cellular maps X → Y and Y → X

1.Evaluate the integral C where C is x=t^3 and y=t, 0 ≤ t ≤ 1
2.Find the area of the surface with vectorial equation r(u,v)=<u,u sinv, cu >, 0 ≤ u ≤ h, 0≤ v ≤ 2pi

3) The Gross method of apportionment works as follows: Assign each state its lower quota. If k states remain to be assigned, then assign them to the k largest states.

a) Does the Gross method satisfy Quota rule?

b) Does the Gross method satisfy Population monotonicity?

Suppose C_t is the concentration of a drug in the bloodstream t hours after the initial dose is administered. Suppose the initial dose C₂was 217.6 ug/mL and suppose that every hour is administered 174 g/mL. If the body metabolizes and eliminates 54% of the concentration of the drug C_t over a period of one hour; determine C₂, the concentration of the drug in the bloodstream two hours after the initial dose is administered.

Response at two decimal valors.

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You buy a sofa for $1499, 2 chairs (each at $299),$249 coffee table,$199 end table, $153 for tax, $75 for delivery. What is the minimum monthly payment using the promotion to the nearest cent?

prove that the product of 2 dilation is either a translation or a dilation

Let G be a group acting on a set S, and let H be a group acting on a set T. The product group G × H acts on the disjoint union S ∪ T as follows. For all g ∈ G, h ∈ H,

s ∈ S and t ∈ T,

(g, h) · s = g · s, (g, h) · t = h · t.

(a) Consider the groups G = C₄, H = C₅, each acting as usual. Calculate the cyclic polynomial Z_C4×C5 .

(b) Explain why in general Z_G×H = Z_GZ_H.