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.

$\bf \cfrac{2}{5+i}\cdot \cfrac{5-i}{5-i}\implies \cfrac{2(5-i)}{\stackrel{\textit{difference of squares}}{(5+i)(5-i)}}\implies \cfrac{2(5-i)}{\stackrel{\textit{recall }i^2=-1}{5^2-i^2}}\implies \cfrac{2(5-i)}{25-(-1)} \\\\\\ \cfrac{2(5-i)}{25+1}\implies \cfrac{2(5-i)}{26}\implies \cfrac{5-i}{13}$

4 0

3 years ago

There were 99 tulips in the field. Only 3/9 bloomed. How many tulips bloomed? How many did not bloom?

Ratling [72]

Answer: 33 tulips bloomed / 66 tulips did not bloom

Step-by-step explanation:

<h2>Given:</h2>

Total number of tulips = 99

Total number of tulips bloomed = 3/9 of total

<h2>Solve:</h2>

Step One: Find the number of tulips that bloomed

99 × (3/9) = 99 × (1/3) = 33 tulips

Step Two: Find the number of tulips that did not bloom

99 - 33 = 66 tulips

Hope this helps!! :)

Please let me know if you have any questions

6 0

3 years ago

A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

marishachu [46]

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

$V = s^2h = 5324$