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A^2/(C-B)=B+C 3^2/1=B+(B+1)=4+5 But 6^2/2=B+(B+1)=18=8+10 does. 5^2/1=25=B+(B+1)=12+13 But 7^2/1=49=B+(B+1)=24+25

Nice circle!

Pivot entrie should be other than 1 in 3rd row how it's possible in row echelon form leading entry is 1 you wrote -4 plz explain this point

Pls do some more problems of eigen values

4.1 x 4.1 = 16.81 4.2 x 4.2 = 17.64 4.125 x 4.125 =17.0156 4.1245 x 4.1245 = 17.0115 4.123 x 4.123 = 16.999 √17 is about 4.123

FYI the doubling the value and using that as the denominator, is just taking the second value of the continued fraction. Also can be found via newton's method.

Great 🎉

Learned this 50 years ago in high school... never had occasion to use it in the real world. However, I did have occasion to use matrix math to do non-linear regression a couple of times about 10 years later. (Imagine storing thermocouple tables in just 5 or 6 floats!) I was never very good at the hand calculations, but I was great at coding it in C. Worked just fine! :)

Thank you for the explanation

Isn't this just a single pass of Newton"s method?

5+3+2+1/2+3/5+1/4 = 10+3/4+3/5 = 10+(15+12)/20 = 10+(20+7)/20 = 11+7/20

about 5+3+2+10/20+12/20+5/20+=11 7/20 or 11 1/4 1/1O with a pencil....?

i i captain. >>;=) Been so long since I fooled with these, but thankfully it comes right back. Like in √-90, or i√90, you know 9*10 for instance; if you know your squares, then you know the 9 is 3² and you can steal the 3 out and leave that 10 behind. It may not stand out so obviously with most numbers though, but can cut down on the amt of factorization you have to do. Full factorization of course guarantees you don't miss anything. Pulling out 2s is quick if you can see the last 2 digits of a # is div by 4.

Why we subtract 1 and add 1later in finding n ??

Many people wonder why radians do not appear when we have radians*meters (rad • m). Here is an attempt at an explanation: Let s denote the length of an arc of a circle whose radius measures r. If the arc subtends an angle measuring β = n°, we can pose a rule of three: 360° _______ 2 • 𝜋 • r n° _______ s Then s = (n° / 360°) • 2 • 𝜋 • r If β = 180° (which means that n = 180, the number of degrees), then s = (180° / 360°) • 2 • 𝜋 • r The units "degrees" cancel out and the result is s = (1 / 2) • 2 • 𝜋 • r s = 𝜋 • r that is, half of the circumference 2 • 𝜋 • r. If the arc subtends an angle measuring β = θ rad, we can pose a rule of three: 2 • 𝜋 rad _______ 2 • 𝜋 • r θ rad _______ s Then s = (θ rad / 2 • 𝜋 rad) • 2 • 𝜋 • r If β = 𝜋 rad (which means that θ = 𝜋, the number of radians), then s = (𝜋 rad / 2 • 𝜋 rad) • 2 • 𝜋 • r The units "radians" cancel out and the result is s = (1 / 2) • 2 • 𝜋 • r s = 𝜋 • r that is, half of the circumference 2 • 𝜋 • r. If we take the formula with the angles measured in radians, we can simplify s = (θ rad / 2 • 𝜋 rad) • 2 • 𝜋 • r s = θ • r where θ denotes the "number of radians" (it does not have the unit "rad"). θ = β / (1 rad) and θ is a dimensionless variable [rad/rad = 1]. However, many consider θ to denote the measure of the angle and for the example believe that θ = 𝜋 rad and radians*meter results in meters rad • m = m since, according to them, the radian is a dimensionless unit. This solves the problem of units for them and, as it has served them for a long time, they see no need to change it. But the truth is that the solution is simpler, what they have to take into account is the meaning of the variables that appear in the formulas, i.e. θ is just the number of radians without the unit rad. Mathematics and Physics textbooks state that s = θ • r and then θ = s / r It seems that this formula led to the error of believing that 1 rad = 1 m/m = 1 and that the radian is a dimensionless derived unit as it appears in the International System of Units (SI), when in reality θ = 1 m/m = 1 and knowing θ = 1, the angle measures β = 1 rad. In the formula s = θ • r the variable θ is a dimensionless variable, it is a number without units, it is the number of radians. When confusing what θ represents in the formula, some mistakes are made in Physics in the units of certain quantities, such as angular speed. My guess is that actually the angular speed ω is not measured in rad/s but in (rad/rad)/s = 1/s = s^(-1).

At minute 0:55 you calculate θ by substituting the arc and radius lengths in the formula θ = s / r θ = (50 m) / (25 m) θ = 2 rad. Actually the result is θ = 2 since θ is a dimensionless variable in the formula, it is the “number of radians”, and the measure of the angle, let's call it β, is You believe like most of the scientific community and the International System of Units (SI) that θ is measured in radians. That is not true. I will write you another comment where I show how the formula is obtained and what the variables represent.

Great video!

why do you name video "how to evaluate natural logarithms" ? these formulas works for any other real positive number (except 1)

Not bad.

@Zach's Math Zone --

great trick thanks

square root of 68 is just 2sqrt(17)

If you’re going to calculate the square root by hand anyway, just use the square root algorithm.

Wow! Really informative and concise.