Math: divisibility by 6
Tutoring math, divisibility rules are useful. The tutor mentions how to determine divisibility by 6. In my post about divisibility by 3 and 9, I mention that if a number is divisible by 3, the sum of its digits is. …
Category: math
Math: an interesting thing about 30
Tutoring math, number exploration is interesting. The tutor mentions 30 as an example of consecutive factors. It’s not new to say that 30 = 5×6. However, the factor set 5×6 is interesting, in a way. In math, n and n+1 …
Math, philosophy: unlikelihood
Self-tutoring about math and life: the tutor mentions an unlikely event. Today I was using a new software package. Naturally enough, I decided to test the random function. It was modelling rolling a die, and I wanted to make sure …
Math, retrospect: walking speed
Self-tutoring about being a pedestrian: the tutor reflects regarding walking speed. When I was a kid, we walked nearly everywhere. We did have bikes, but used them more for planned, return trips. For just going “out,” nowhere in particular, we …
Math: fun with prime factorization
Tutoring math, you notice interesting details. The tutor mentions one. Fact: 42 goes into 252. One might not notice, as first, that 42 goes into 252. However, 9 does (2+5+2=9); dividing, we see that 9×28=252. From there, one can break …
Math: why sin(180° – x) = sinx
Tutoring math, trig identities are important. The tutor mentions one. An identity, meaning something always true, is sin(a – b) = sin(a)cos(b) – cos(a)sin(b) Therefore, sin(180° – x) = sin(180°)cos(x) – cos(180°)sin(x) Since sin(180°) = 0 and cos(180°) = -1 …
Math: solutions to sin equations
Tutoring math, you see trig equations. The tutor mentions some top-down ideas. Considering the equation sinx=K, for K ε Reals sinx = sin(180°-x), 0≤x<90°. Therefore, if the equation has a solution θ between 0 and 90°, it will typically have …
Math: the inverse, part 1
Tutoring math, inverses come up. The tutor begins about them. Simply put, an inverse takes (x,y) and makes it (y,x). If f(x) yields y, then f-1(y) yields x. To get the inverse algebraically, one interchanges x with y. For instance, …
Math: novelty factoring, part 1
Tutoring math, factoring is a typical topic. The tutor mentions a novelty. In this post, x^n means xn Sometimes, one can factor third degree polynomials of the form ax^3 +bx^2 +cx + d without using the remainder theorem, synthetic division, …
Math: word problems: “let” statements
Tutoring math, word problems come up. The tutor gives an example of “let” statements. Problem: A 207cm rope is cut in two pieces, one 15cm longer than the other. How long is each piece? Solution: “let” statements are used to …