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ludmilkaskok [199]
3 years ago
12

I need help like RN!!! what are the foci of the ellipse? graph the ellipse. 18x^2+36y^=648

Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
7 0
Hi,

18x^2+36y^2=648\\

\Rightarrow ( \dfrac{x}{6})^2+( \dfrac{y}{3* \sqrt{2} } )^2=1\\

a=6,\ b=3* \sqrt{2}\\

c= \sqrt{a^2-b^2} = \sqrt{36-18} =3* \sqrt{2}\\


Center is (0,0)
Foci are (-3√2,0) and (3√2,0)

Lerok [7]3 years ago
6 0

Answer:

The equation of ellipse is given by:

\frac{x^2}{a^2}+\frac{y^2}{b^2} =1                 ....[1]

where,

a and b are the semi major axis and semi minor axis.

Foci of ellipse = (\pm c, 0)

where, c = \sqrt{a^2-b^2}

As per the statement:

Given the ellipse is:

18x^2+36y^2 = 648

Divide both sides by 648 we have;

\frac{x^2}{36}+\frac{y^2}{18} =1

On comparing with [1] we have;

a^2 =36 and b^2=18

First find c:

c = \sqrt{36-18}=\sqrt{18}=3\sqrt{2}

Foci of the ellipse are:

(\pm 3\sqrt{2}, 0)

Therefore, the foci of the ellipse are, (3\sqrt{2}, 0) and (-3\sqrt{2} , 0)

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Given:

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For us to be able to determine the population in 2022, we will be using the following formula:

\text{ P = P}_0e^{rt}

Where,

P = Total population after time (t)

P₀ = Starting population = 4.18 million

r = Growth rate (in decimal form) = 6.2%/100 = 0.062

t = time (in years) = 2022 - 2016 = 6 years

e = Euler's number = 2.71828182845

We get,

\text{ P = P}_0e^{rt}\text{ = (4,180,000)(}2.71828182845)^{0.062(6)}\text{ P = 6,063,645.861797897 }\approx\text{ 6,063,646}

Therefore, the population in 2022 will be approximately 6,063,646.

7 0
1 year ago
200 students in a high school senior class are surveyed about what majors they intend to declare in college. Of the 200 students
True [87]

Answer:

  • <u><em>P(M) = 0.4</em></u>

Explanation:

<u>1. Build a two-way frequency table:</u>

To have a complete understanding of the scenary build a two-way frequency table.

  • <u>Column and rows:</u>

                                  Major in math    No major in math  Total

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No major in CS

Total

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                                  Major in math    No major in math  Total

Major in CS

No major in CS

Total                                                                                      200

  • <u>80 plan to major in mathematics:</u>

                                  Major in math    No major in math  Total

Major in CS

No major in CS

Total                              80                                                   200

  • <u>100 plan to major in computer science</u>:

                                  Major in math    No major in math  Total

Major in CS                                                                           100

No major in CS

Total                              80                                                   200

  • <u>30 plan to pursue a double major in mathematics and computer science</u>:

                                  Major in math    No major in math  Total

Major in CS                  30                                                      100

No major in CS

Total                              80                                                    200

  • <u>Complete the missing numbers by subtraction</u>:

                                  Major in math    No major in math  Total

Major in CS                   30                              70                 100

No major in CS                                                                     100

Total                              80                             120                200

                                  Major in math    No major in math  Total

Major in CS                   30                              70                 100

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