namely, let's rationalize the denominator in the fraction, for which case we'll be using the <u>conjugate</u> of that denominator, so we'll multiply top and bottom by its <u>conjugate</u>.
so the denominator is 5 + i, simply enough, its conjugate is just 5 - i, recall that same/same = 1, thus (5-i)/(5-i) = 1, and any expression multiplied by 1 is just itself, so we're not really changing the fraction per se.
![\bf \cfrac{2}{5+i}\cdot \cfrac{5-i}{5-i}\implies \cfrac{2(5-i)}{\stackrel{\textit{difference of squares}}{(5+i)(5-i)}}\implies \cfrac{2(5-i)}{\stackrel{\textit{recall }i^2=-1}{5^2-i^2}}\implies \cfrac{2(5-i)}{25-(-1)} \\\\\\ \cfrac{2(5-i)}{25+1}\implies \cfrac{2(5-i)}{26}\implies \cfrac{5-i}{13}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B2%7D%7B5%2Bi%7D%5Ccdot%20%5Ccfrac%7B5-i%7D%7B5-i%7D%5Cimplies%20%5Ccfrac%7B2%285-i%29%7D%7B%5Cstackrel%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%285%2Bi%29%285-i%29%7D%7D%5Cimplies%20%5Ccfrac%7B2%285-i%29%7D%7B%5Cstackrel%7B%5Ctextit%7Brecall%20%7Di%5E2%3D-1%7D%7B5%5E2-i%5E2%7D%7D%5Cimplies%20%5Ccfrac%7B2%285-i%29%7D%7B25-%28-1%29%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B2%285-i%29%7D%7B25%2B1%7D%5Cimplies%20%5Ccfrac%7B2%285-i%29%7D%7B26%7D%5Cimplies%20%5Ccfrac%7B5-i%7D%7B13%7D)
Answer:
5.0-2.5=2.5
Step-by-step explanation:
Answer:The equation relating I, r, and k is I =K/r²
Step-by-step explanation:
The intensity, I, of a sound varies inversely with the square of the distance, r, from the source of the sound can be written as
I ∝ 1/r²
Introducing the constant of proportionality, K we have that
I =K x 1/r²
Therefore , the equation relating I, r, and k is I =K/r²
Answer:
Step-by-step explanation:
hello
calculate x : 3x+2 =5
means : 3x+2-2 =5-2
3x = 3
so : x = 3/3 =1
1 is the element in domain has the image 5 under function f(x)= 3x+ 2