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belka [17]
3 years ago
9

FIRST TO ANSWER GETS BRAINLIEST AND 5 POINTS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~
What is the graph of y>|x-3|?

Mathematics
1 answer:
pantera1 [17]3 years ago
3 0

Answer:

It is the first graph

Step-by-step explanation:

Since it is an inequality you'd know that the lines are going to be dotted like in the first option. And since the equation is not true, you have to shade in the top region and not the rest of the region.

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Solve the equation in the interval [0,2π]. If there is more than one solution write them separated by commas.
Sedaia [141]
\large\begin{array}{l} \textsf{Solve the equation for x:}\\\\ &#10;\mathsf{(tan\,x)^2+2\,tan\,x-4.76=0}\\\\\\ \textsf{Substitute}\\\\ &#10;\mathsf{tan\,x=t\qquad(t\in \mathbb{R})}\\\\\\ \textsf{so the equation &#10;becomes}\\\\ \mathsf{t^2+2t-4.76=0}\quad\Rightarrow\quad\begin{cases} &#10;\mathsf{a=1}\\\mathsf{b=2}\\\mathsf{c=-4.76} \end{cases} &#10;\end{array}


\large\begin{array}{l} \textsf{Using &#10;the quadratic formula:}\\\\ \mathsf{\Delta=b^2-4ac}\\\\ &#10;\mathsf{\Delta=2^2-4\cdot 1\cdot (-4.76)}\\\\ &#10;\mathsf{\Delta=4+19.04}\\\\ \mathsf{\Delta=23.04}\\\\ &#10;\mathsf{\Delta=\dfrac{2\,304}{100}}\\\\ &#10;\mathsf{\Delta=\dfrac{\diagup\!\!\!\! 4\cdot 576}{\diagup\!\!\!\! 4\cdot&#10; 25}}\\\\ \mathsf{\Delta=\dfrac{24^2}{5^2}} \end{array}

\large\begin{array}{l}&#10; \mathsf{\Delta=\left(\dfrac{24}{5}\right)^{\!2}}\\\\ &#10;\mathsf{\Delta=(4.8)^2}\\\\\\ &#10;\mathsf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\ &#10;\mathsf{t=\dfrac{-2\pm\sqrt{(4.8)^2}}{2\cdot 1}}\\\\ &#10;\mathsf{t=\dfrac{-2\pm 4.8}{2}}\\\\ \mathsf{t=\dfrac{\diagup\!\!\!\! &#10;2\cdot (-1\pm 2.4)}{\diagup\!\!\!\! 2}}\\\\\mathsf{t=-1\pm 2.4} &#10;\end{array}

\large\begin{array}{l} \begin{array}{rcl} &#10;\mathsf{t=-1-2.4}&~\textsf{ or }~&\mathsf{t=-1+2.4}\\\\ &#10;\mathsf{t=-3.4}&~\textsf{ or }~&\mathsf{t=1.4} \end{array} &#10;\end{array}


\large\begin{array}{l} \textsf{Both &#10;are valid values for t. Substitute back for }\mathsf{t=tan\,x:}\\\\ &#10;\begin{array}{rcl} \mathsf{tan\,x=-3.4}&~\textsf{ or &#10;}~&\mathsf{tan\,x=1.4} \end{array}\\\\\\ \textsf{Take the inverse &#10;tangent function:}\\\\ \begin{array}{rcl} &#10;\mathsf{x=tan^{-1}(-3.4)+k\cdot \pi}&~\textsf{ or &#10;}~&\mathsf{x=tan^{-1}(1.4)+k\cdot \pi}\\\\ &#10;\mathsf{x=-tan^{-1}(3.4)+k\cdot \pi}&~\textsf{ or &#10;}~&\mathsf{x=tan^{-1}(1.4)+k\cdot \pi} \end{array}\\\\\\ &#10;\textsf{where k in an integer.} \end{array}

__________


\large\begin{array}{l}&#10; \textsf{Now, restrict x values to the interval &#10;}\mathsf{[0,\,2\pi]:}\\\\ \bullet~~\textsf{For }\mathsf{k=0:}\\\\ &#10;\begin{array}{rcl} &#10;\mathsf{x=-tan^{-1}(3.4)


\large\begin{array}{l}&#10; \bullet~~\textsf{For }\mathsf{k=1:}\\\\ \begin{array}{rcl} &#10;\mathsf{x=-tan^{-1}(3.4)+\pi}&~\textsf{ or &#10;}~&\mathsf{x=tan^{-1}(1.4)+\pi} \end{array}\\\\\\ &#10;\boxed{\begin{array}{c}\mathsf{x=-tan^{-1}(3.4)+\pi} &#10;\end{array}}\textsf{ is in the 2}^{\mathsf{nd}}\textsf{ quadrant.}\\\\ &#10;\mathsf{x\approx 1.86~rad~~(106.39^\circ)}\\\\\\ &#10;\boxed{\begin{array}{c}\mathsf{x=tan^{-1}(1.4)+\pi} \end{array}}\textsf{&#10; is in the 3}^{\mathsf{rd}}\textsf{ quadrant.}\\\\ \mathsf{x\approx &#10;4.09~rad~~(234.46^\circ)}\\\\\\ \end{array}


\large\begin{array}{l}&#10; \bullet~~\textsf{For }\mathsf{k=2:}\\\\ \begin{array}{rcl} &#10;\mathsf{x=-tan^{-1}(3.4)+2\pi}&~\textsf{ or &#10;}~&\mathsf{x=tan^{-1}(1.4)+2\pi>2\pi~~\textsf{(discard)}} &#10;\end{array}\\\\\\ \boxed{\begin{array}{c}\mathsf{x=-tan^{-1}(3.4)+2\pi} &#10;\end{array}}\textsf{ is in the 4}^{\mathsf{th}}\textsf{ quadrant.}\\\\ &#10;\mathsf{x\approx 5.00~rad~~(286.39^\circ)} \end{array}


\large\begin{array}{l}&#10; \textsf{Solution set:}\\\\ &#10;\mathsf{S=\left\{tan^{-1}(1.4);\,-tan^{-1}(3.4)+\pi;\,tan^{-1}(1.4)+\pi;\,-tan^{-1}(3.4)+2\pi\right\}}&#10; \end{array}


<span>If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2071152</span>


\large\textsf{I hope it helps.}


Tags: <em>trigonometric trig quadratic equation tangent tan solve inverse symmetry parity odd function</em>

6 0
3 years ago
a falcon can fly at a speed of 87 kilometers per hour. a goose can fly at a speed of 78 kilometers per hour. Suppose a falcon an
RoseWind [281]

Answer:

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MaRussiya [10]

Answer:

x=13/5

Step-by-step explanation:

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