For these problems you have to use PEMDAS so for problem 15 you would do the parentheses first, (21-3) you get 18 and then exponents, 3^2, you get 9, no multiplication but there is division so take your answers, 18 and 9 and divide them, you get 2, so the answer to 15 is 2.
Answer:
sqrt(-8x+5)
Step-by-step explanation:
(5-8x)
-----------------
sqrt(-8x+5)
We need to rationalize the denominator
(5-8x) sqrt(-8x+5)
----------------- * ---------------
sqrt(-8x-5) sqrt(-8x+5)
(5-8x) sqrt(-8x+5)
----------------- * ---------------
(-8x+5)
The first term cancels
sqrt(-8x+5)
Answer:
Step-by-step explanation:
Answer:The equation for inverse proportion is x y = k or x = k/ y. Therefore, for finding the value of the constant k, you can use the known values and then use this formula to calculate all the unknown values.
(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)
… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)
… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))
… = (2 - 2√3 <em>i</em> ) / 4
… = 1/2 - √3/2 <em>i</em>
… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))
… = exp(<em>i</em> arctan(-√3))
… = exp(-<em>i</em> arctan(√3))
… = exp(-<em>iπ</em>/3)
By DeMoivre's theorem,
[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1
