## Online Course Discussion Forum

### Could someone help with winter camp blue algebra p20-23?

Here's a few hints to get you started:

- 20: Use a substitution to turn the equation into a quadratic.
- 21: Number the equations $(1)$, $(2)$, and $(3)$, and the desired expression $(4$). Find values of $a$, $b$ and $c$ such that (the left sides of satisfy) $a(1) + b(2) + c(3) = (4)$.
- 22: Use a substitution $y = x\sin(x)$, then use AM-GM inequality.

Having the same questions as Iris, I read these hints, but I can not understand them.

For 20, we are not multiplying anything at all, so I do not see how it could be turned into a quadratic, even with a substitution.

For 21, we are given only given 2^(1 + floor(log_2 (N-1))) - N = 19, and I do not see which equations to label.

For 22, we are given a function which does not mention sin at all, and I cannot see how to apply sin in this scenario.

Given that these are not relevant to 20-22 of the other Blue Practice Problems, think that these are meant for Green Practice Problems instead of the Blue ones. May the Professor please double check? Or am I interpreting these hints incorrectly?

Sorry, the previous hints were for different questions. Here are real hints:

P20: For questions involving absolute values, the first thing to do is to see how to resolve the absolute values. Sometimes casework is needed. In this question, the sign for each absolute value is already determined, so no casework is necessary.

P21: Set up an equation $2^{1+\lfloor{\log_2 (N-1)}\rfloor} - N = 19$, then add $N$ on both sides and take the log (base $2$). With the floor function, this comes down to an inequality about $N$.

P22: Draw the graph of $f(x)$ in the interval $[1,3]$, and then the interval $[3,9]$, and so on.

P23: This is a system of linear equations, which is not hard to solve.

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