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Algebra

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 4π³ββ¬=π³β¬+2π if π=(β2141), β¬=(71β72).

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

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3. Solve the system of linear equations: π₯β2π¦+π§=5,β2π₯+3π¦βπ§=β8,βπ₯βπ¦+2π§=2.

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4. Calculate the area of the flat shape bounded by the curves: π¦=βπ₯β1,π¦=3βπ₯,π¦=0.

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5. Find all the extrema of the function π(π₯)=β16βπ₯2.

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

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Algebra

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

Algebra

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

1. Find the domain of the function π(π₯)=ln(β2π₯2βπ₯β6)+βπ₯2β1.

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2. Find the inverse function of the function π(π₯)=π₯2β4π₯+5,π₯βγ3,4β©. 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 π(π₯)=4π₯β βπ₯β2β βπ₯ which is parallel to the line π¦=π₯.

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4. Find the maximal intervals of monotonicity of the function π(π₯)=ππ₯+3π₯2+2π₯+6.

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5. Find the integral β«6β π₯3β ππ₯2+2ππ₯.

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6. Find the general solution of the differential equation π₯2+1+π¦β²β cos(π¦)=0.Β

Algebra

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?

Algebra

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

x^{2} + y^{2} = 5

x + y = 1

Algebra

Solve this system of equations.

(x + 1)^{2} + (y + 1)^{2} = 25,x + y = 5

Algebra

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.

Algebra

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

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