zoejacobs2002

13.03.2021 •

Mathematics

The Vikings basketball team score the points shown below in the last seven games. Which box plot best represents the Vikings basketball scores?

The Vikings basketball team score the points shown below in the last seven games. Which box plot be

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Ответ:

ldibut2003

08.07.2021

Mathematics

correct answer is option 3:

$\dfrac{x^{2} }{30}+\dfrac{y^{2} }{5}=1$

Step-by-step explanation:

Given that

Ellipse passes through coordinates:

$\approx (5\dfrac{1}{2},0),\approx (-5\dfrac{1}{2},0), \approx (0,2)\ and\ \approx (0,-2)$

Points inside ellipse (5, 0) and (-5,0).

Given the options:

$1.\ \dfrac{x^{2} }{5}+\dfrac{y^{2} }{30}=1\\2.\ \dfrac{x^{2} }{5}-\dfrac{y^{2} }{30}=1\\3.\ \dfrac{x^{2} }{30}+\dfrac{y^{2} }{5}=1\\4.\ \dfrac{x^{2} }{30}+\dfrac{y^{2} }{25}=1\\$

Let us try to put the coordinates in the options and check which equation gets satisfied.

Putting x = 0, and trying to find out y in option 1.

$\ \dfrac{0^{2} }{5}+\dfrac{y^{2} }{30}=1\\\Rightarrow \dfrac{y^{2} }{30}=1\\\Rightarrow y =\pm\sqrt{30} \approx \pm5\dfrac{1}{2}$

But, the points are $\approx (5\dfrac{1}{2},0),\approx (-5\dfrac{1}{2},0), \approx (0,2)\ and\ \approx (0,-2)$

So, option (1) is false.

Putting x = 0 to find y in option 2.

$\ \dfrac{0^{2} }{5}-\dfrac{y^{2} }{30}=1\\\Rightarrow \dfrac{y^{2} }{30}=-1$

y will have imaginary values so ellipse not possible at x = 0.

So, option (2) is false.

Putting x = 0 to find y in option 3.

$\ \dfrac{0^{2} }{30}+\dfrac{y^{2} }{5}=1\\\Rightarrow \dfrac{y^{2} }{5}=1\\\Rightarrow y \approx \pm2$

Putting y = 0 to find y in option 3.

$\ \dfrac{x^{2} }{30}+\dfrac{0^{2} }{5}=1\\\Rightarrow \dfrac{x^{2} }{30}=1\\\Rightarrow x \approx \pm5\dfrac{1}{2}$

So, the points $\approx (5\dfrac{1}{2},0),\approx (-5\dfrac{1}{2},0), \approx (0,2)\ and\ \approx (0,-2)$ are satisfied.

Putting (5, 0) and (-5,0) in LHS of option 3:

$\ \dfrac{(\pm5)^{2} }{30}+\dfrac{0 }{5}\\\Rightarrow \dfrac{25} {30}\\\Rightarrow \dfrac{5}{6}$

i.e. both the points are inside ellipse.

Hence correct answer is option 3:

$\dfrac{x^{2} }{30}+\dfrac{y^{2} }{5}=1$

Which of the following is the equation for the graph shown?

graph of an ellipse on a coordinate pla

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