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$\frac{20b}{{\left(4b^3\right)}^3}$

1. A body falls from rest against resistance proportional to the square root of the speed at any instant. If the body attains speed V1 and V2 feet per second, after 1 and 2 seconds in motion, respectively, find an expression for the limiting velocity.

Question 71

22+64

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Derivatives Find and simplify the derivative of the following functions
${\displaystyle p\left(x\right)=\frac{4x^3+3x+1}{2x^5}}$

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If $a+b$ is an irrational number. Is $a-b$ an irrational number, too?

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Calculate $$\sqrt{3}(5-3\sqrt{5})$$

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Find the derivative using the product rule.
${\displaystyle y=e^x\ln x}$

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truggling with these problems, which I believe are both cases of pigeonhole principle but I am struggling to get the right answer.
1) An IT survey asks desktop computer users the following questions: -- which OS type they are using (Windows, macOS, Linux, other) -- if Windows: Windows 10, 8.1, 7 or other -- if macOS: 10.12, 10.11, lower -- if Linux: Mint, Debian, Ubuntu, other -- screen resolution used (lower, equal or higher than 1920x1080) -- whether they play games on their desktop (yes/no) How many people have to be asked to guarantee that you will find 10 with identical answers?
2) How many subsets are there of a set of 100 elements that contain at least 4 elements? You must simplify your answer until it contains only unresolved large exponential expressions of the form 𝑎 𝑏 with a and b integers.

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Solve $$x^3=2x^2+35x$$ by factoring and using the zero product property

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The system is as follows:
$$\begin{array}{rl}{i}_1& =i_2+i_3,\\ 50\sin t& =6i_1+i_2^{\prime }+5i_2,\\ 50\sin t& =6i_1+i_3^{\prime },\end{array}$$
Find $i_2,i_3$.

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