When the population is large, researchers usually select a sample and study it instead of studying the entire population. In this case, the way that the sample is selected is Important. Explain why and how that the way the sample is selected is important. Give an example to illustrate your answer

Solved

Show answers

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

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice