$when \: \: \sqrt{3} \sin( \alpha ) - \cos( \alpha ) = 0 \\ \sqrt{3} \sin( \alpha ) = \cos( \alpha ) \\ multiply \: by \: \frac{1}{ \sqrt{3} \cos( \alpha ) } \\ then \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \frac{1}{ \sqrt{3} } \\ \tan( \alpha ) = \frac{1}{ \sqrt{3} } \\ then \: \alpha = 30$

3 0

3 years ago

Dividing rational expressions

Galina-37 [17]

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
\cfrac{x+3}{x^2-2x}\cdot \cfrac{(x-2)^2}{x^2-9}\implies \cfrac{x+3}{x^2-2x}\cdot \cfrac{(x-2)(x-2)}{x^2-3^2}
\\\\\\
\cfrac{x+3}{x(x-2)}\cdot \cfrac{(x-2)(x-2)}{x^2-3^2}\implies \cfrac{\underline{x+3}}{x\underline{(x-2)}}\cdot \cfrac{\underline{(x-2)}(x-2)}{(x-3)\underline{(x+3)}}
\\\\\\
\cfrac{x-2}{x(x-3)}\iff\cfrac{x-2}{x^2-3x}$

5 0

3 years ago

Identify the horizontal translation of the parent function f(x) = x^2<br> Y= (x+5)^2

qaws [65]

It will translate 5 to the left.

5 0

3 years ago

If the part is 63 and the percent is 90% what is the whole plz help

Crazy boy [7]

Answer:

Step-by-step explanation:

63/9 = 7

7 * 10 = 70

3 0

3 years ago