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Ch3 HW2

$\newcommand{\abs}[1]{\lvert{#1}\rvert}$

The purpose of this homework is to practice working with loop. There is starter code to download, also available at the end of this document.

(one-more-mult) Make sure you know how to use (mod x n) to figure out if x is divisible by n. Write a function that takes in an integer and returns true when the integer is one more than a multiple of 8.
(all-6-by-17) Given a list of integers, return all of the elements that are either greater than 100 or leave a remainder of 6 when divided by 17.
(long-words) Given a list of words, return the number of words in the list that are longer than 6 letters.
(good-lists) Given a list of lists ys, if a sublist y of ys begins with the symbol GOOD, then put every element from the list y in the answer.

Working with pairs

In all of the following problems, you are given a list of ordered pairs of numbers, like (list 5 12).

(x010) Return a list of all of the x values that are in the interval [0,10].
(y200) Return a list of all of the points whose y values are either greater than 200 or less than -200.
(ptf) Find the greatest value of $f(x,y) = x^2 + 3 y^2 - 2 x y$ using the points in the list.
(smd) Find the smallest difference $\abs{x-y}$ in the list.
(aop) If every point is on the parabola $y=x^2$ then return true (otherwise false).
(isfar) If any point has $\abs{y - x^2} > 10$, then return true.
(not10x) If no point in the list has $y = 10^x$, return true.

(xyzTrip) Given a list of triples $(x,y,z)$, which we write (list x y z), return a list containing (list x y) for every point where $z=x^2+y^2$.