Tutoring math, problems might come up about the turns (rpm) of one gear relative to another. The tutor mentions an example. Question: Suppose Gear A (14 teeth) and Gear B (21 teeth) are enmeshed. If Gear B turns 60 rpm, …
Math: how fast does one gear turn, if the other gear turns at so-and-so rpm? Read more »
Self-tutoring about yard work: the tutor relates it to exponential decay. Yesterday was an incredible day here, especially given the forecast. It was bright and sunny, with a temp that reached over ten degrees Celsius. Naturally I went out into …
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. …
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 …
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 …
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 …
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 …
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 …
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 …
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, …