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Category: math

Math: how fast does one gear turn, if the other gear turns at so-and-so rpm?

By Jack Posted on February 9, 2025 Posted in math Tagged with gear, rpm

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, …

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Yard work, math: half-life of a cleanup?

By Jack Posted on November 10, 2024 Posted in math, yard work Tagged with cleanup

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 …

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Math: divisibility by 6

By Jack Posted on August 6, 2024 Posted in math Tagged with 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. …

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Math: an interesting thing about 30

By Jack Posted on August 5, 2024 Posted in math Tagged with consecutive factors, number exploration

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 …

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Math, philosophy: unlikelihood

By Jack Posted on June 15, 2024 Posted in math, philosophy

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 …

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Math, retrospect: walking speed

By Jack Posted on June 4, 2024 Posted in lifestyle, math, retrospect Tagged with 2 miles per hour walking speed, casual walking speed, typical 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 …

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Math: fun with prime factorization

By Jack Posted on May 12, 2024 Posted in math Tagged with divisibility, prime factorization, times tables

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 …

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Math: why sin(180° – x) = sinx

By Jack Posted on April 30, 2024 Posted in math Tagged with sin function, sine function, trig identities

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 …

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Math: solutions to sin equations

By Jack Posted on April 27, 2024 Posted in math Tagged with sin function, sine function, trig 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 …

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Math: the inverse, part 1

By Jack Posted on April 15, 2024 Posted in math Tagged with inverse

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, …

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