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On a website that sells funny T-shirts, the number of customers has been falling 10% per month. If the site had 14,000 customers this month, then how many should it expect to have 10 months from now?


1. Solve the matrix equation 4π’³βˆ’β„¬=𝒳ℬ+2π’œ if π’œ=(βˆ’2141), ℬ=(71βˆ’72).

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2. Calculate the inverse matrix to the matrix π’œ=(001011111). Check whether the obtained inverse matrix is correct.

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3. Solve the system of linear equations: π‘₯βˆ’2𝑦+𝑧=5,βˆ’2π‘₯+3π‘¦βˆ’π‘§=βˆ’8,βˆ’π‘₯βˆ’π‘¦+2𝑧=2.

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4. Calculate the area of the flat shape bounded by the curves: 𝑦=√π‘₯βˆ’1,𝑦=3βˆ’π‘₯,𝑦=0.

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5. Find all the extrema of the function 𝑓(π‘₯)=√16βˆ’π‘₯2.

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6. Find the maximal intervals of convexity (concavity) of the function 𝑓(π‘₯)=2π‘₯+arctg(3π‘₯). Find the respective inflection points.

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f(t)= 1+0.12t, compute f(t) if t=2.


How many 5mb mp3 files can be stored on a 1gb flash drive?


1. Find the domain of the function 𝑓(π‘₯)=ln(βˆ’2π‘₯2βˆ’π‘₯βˆ’6)+√π‘₯2βˆ’1.

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2. Find the inverse function of the function 𝑓(π‘₯)=π‘₯2βˆ’4π‘₯+5,π‘₯βˆˆγ€ˆ3,4⟩. Find the domain and the range of the inverse function.

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3. Construct the tangent line to the graph of the function 𝑓(π‘₯)=4π‘₯β‹…βˆšπ‘₯βˆ’2β‹…βˆšπ‘₯ which is parallel to the line 𝑦=π‘₯.

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4. Find the maximal intervals of monotonicity of the function 𝑓(π‘₯)=𝑒π‘₯+3π‘₯2+2π‘₯+6.

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5. Find the integral ∫6β‹…π‘₯3⋅𝑒π‘₯2+2𝑑π‘₯.

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6. Find the general solution of the differential equation π‘₯2+1+𝑦′⋅cos(𝑦)=0.Β 


An element with mass 140 grams decays by 21.6% per minute. How much of the element is remaining after 20 minutes, to the nearest 10th of a gram?


Solve this system of equations and provide a graphical representation of the solution. (12)


x2 + y2 = 5


x + y = 1


Solve this system of equations.

(x + 1)2 + (y + 1)2 = 25,x + y = 5


Klipatrick etc Al (2001) came up with five strands or components of mathematical proficiency.Show step by step how you as a teacher can lead learner's towards procedural fluency with conceptual understanding when they convert the decimal fraction 0.25 to common fraction 1/4.Make use of some visual aid like a number line or place value chart support your verbal explanations.


1. Teaching long division of 357Γ·19 for instrumental understanding

2. Teaching long division of 357Γ·19 for relational understanding





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