$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^3y^5)^{\frac{4}{3}}\implies \left( x^{3\cdot \frac{4}{3}}y^{5\cdot \frac{4}{3}} \right)\implies x^4y^{\frac{20}{3}}\implies x^4 y^{\frac{18}{3}+\frac{2}{3}}\implies x^4 y^{\frac{18}{3}} y^{\frac{2}{3}} \\\\\\ x^4y^6 y^{\frac{2}{3}}\implies x^4y^6\sqrt[3]{y^2}$

5 0

4 years ago

Match the function with its graph. a. 1C, 2B, 3D, 4A c. 1D, 2A, 3C, 4B b. 1A, 2D, 3B, 4C d. 1A, 2B, 3C, 4D Please select the bes

oksano4ka [1.4K]

Answer:

The correct answer is "Option C".

Step-by-step explanation:

Given:

$\bold{ 1) y= -\tan (x- \frac{\pi}{2})}\\\\\bold{ 2) y= \tan (x+ \frac{\pi}{2})}\\\\\bold{ 3) y= -\cot (x- \frac{\pi}{2})}\\\\\bold{ 4) y= \cot (x+ \frac{\pi}{2})}\\\\$

solve the above equation:

$\Rightarrow 1) \ y= -\tan (x- \frac{\pi}{2})\\\\\Rightarrow \ y= \tan (\frac{\pi}{2}-x)\\\\\Rightarrow \ y= \cot x \ \ \ \ \ \bold{ that \ matchs \ graph \ D}\\\\ \Rightarrow 2) \ y= \tan (x+ \frac{\pi}{2})\\\\\Rightarrow \ y= - \cot x \ \ \ \ \bold{ that \ matchs \ graph \ A}\\\\$

$\Rightarrow 3) \ y= -\cot (x- \frac{\pi}{2})\\\\\Rightarrow \ y=\cot ( \frac{\pi}{2}-x)\\\\\Rightarrow \ y=\tan x\ \ \ \ \bold{that \ matchs \ graph \ C}\\\\$

$\Rightarrow 4) \ y= \cot (x+ \frac{\pi}{2})\\\\\Rightarrow \ y= \cot (\frac{\pi}{2}+x)\\\\\Rightarrow \ y= \ -tan x \ \ \ \ \ \bold{ that \ matchs \ graph \ A}$

The final answer is "Option C".

8 0

3 years ago