Algebra Answers

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 4𝒳−ℬ=𝒳ℬ+2𝒜 if 𝒜=(−2141), ℬ=(71−72).

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

3. Solve the system of linear equations: 𝑥−2𝑦+𝑧=5,−2𝑥+3𝑦−𝑧=−8,−𝑥−𝑦+2𝑧=2.

4. Calculate the area of the flat shape bounded by the curves: 𝑦=√𝑥−1,𝑦=3−𝑥,𝑦=0.

5. Find all the extrema of the function 𝑓(𝑥)=√16−𝑥2.

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

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(𝑥)=ln(−2𝑥2−𝑥−6)+√𝑥2−1.

2. Find the inverse function of the function 𝑓(𝑥)=𝑥2−4𝑥+5,𝑥∈〈3,4⟩. Find the domain and the range of the inverse function.

3. Construct the tangent line to the graph of the function 𝑓(𝑥)=4𝑥⋅√𝑥−2⋅√𝑥 which is parallel to the line 𝑦=𝑥.

4. Find the maximal intervals of monotonicity of the function 𝑓(𝑥)=𝑒𝑥+3𝑥2+2𝑥+6.

5. Find the integral ∫6⋅𝑥3⋅𝑒𝑥2+2𝑑𝑥.

6. Find the general solution of the differential equation 𝑥2+1+𝑦′⋅cos(𝑦)=0. 

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?

1. Teaching long division of 357÷19 for instrumental understanding

2. Teaching long division of 357÷19 for relational understanding