In the second step, they factored out K.… I don't understand the second and the third steps.
This is not correct. You need to use proper grouping symbols, to show the correct order of operations. Your typing actually means this:w = root (K/m) - (r^2/4m^2)
How to calculate w = root (K/m) - (r^2/4m^2)? Here I don't understand the second and the third steps. Could you simplify the steps for me, please?
Could you suggest me how to write the proper symbols because the keyboard does not have any scientific symbols?In the second step, they factored out K.
In the third step, they factored out 1/m.
Do you need help finding online lessons, to learn how to factor?
This is not correct. You need to use proper grouping symbols, to show the correct order of operations. Your typing actually means this:
\(\displaystyle w = \sqrt{\dfrac{K}{m}} - \dfrac{r^{2}}{4} \cdot m^{2}\)
The correct notation is:
w = sqrt[K/m - r^2/(4m^2)]
Could you simplify this step, please?First, let's be sure to write it correctly; they are staring with sqrt[(K/m) - (r^2)/(4m^2)], where the bar over the radicand has to be replaced with some sort of bracket when we write inline. And we need parentheses around the denominator to make sure that is multiplied first.
Now, the first couple steps are factoring K/m out of the radicand. Here is one way you might think about it (doing it all in one, rather than first factoring out K and then 1/m as they do); a key step is to recognize that multiplying by K/m and also by its reciprocal leaves the value unchanged:
K/m - (r^2)/(4m^2) = (K/m)*1 - (K/m)*(m/K)*(r^2)/(4m^2) [here I rewrote each term with (K/m) as a factor]
= (K/m)[1 - (m/K)(r^2)/(4m^2)] [here I factored out the common factor]
= (K/m)[1 - (1/K)(r^2)/(4m)] [here I canceled an m]
= (K/m)[1 - (r^2)/(4mK)] [here I multiplied the denominators]
Then they can use the fact that (r^2)/(mK) = 0.08.
Sometimes, I use Windows' Character Map, to paste symbols:Could you suggest me how to write the proper symbols … ?
Could you simplify this step, please?
(K/m)[1 - (r^2)/(4mK)] [here I multiplied the denominators] to (r^2)/(mK) = 0.08.