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3 years ago

Aubree took a taxi from her house to the airport. The taxi company charged a pick-up

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

6 0

The taxi ride was 21 miles

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Write an equation for an ellipse centered at the origin, which has foci at (\pm8,0)(±8,0)left parenthesis, plus minus, 8, comma,

mario62 [17]

Answer:

The equation of the ellipse is $\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1$

Step-by-step explanation:

The standard form of the equation of an ellipse with center (0 , 0) is

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ , where

The coordinates of the vertices are (± a , 0)

The coordinates of the foci are (± c , 0) , where c ² = a² - b²

∵ The ellipse is centered at the origin

∴ The center of it is (0 , 0)

∵ It has foci at (± 8 , 0)

- The coordinates of the foci are (± c , 0)

∴ c = ±8

∵ It has Vertices at (± 17 , 0)

- The coordinates of the vertices are (± a , 0)

∴ a = ±17

∵ c² = a² - b²

- Substitute the values of c and a to find b

∴ (8)² = (17)² - b²

∴ 64 = 289 - b²

- Add b² to both sides

∴ b² + 64 = 289

- Subtract 64 from both sides

∴ b² = 225

- Take √ for both sides

∴ b = ± 15

∵ The equation of the ellipse is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

- Substitute the values of a and b in it

∴ $\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1$ ⇒ $\frac{x^{2}}{289}+\frac{y^{2}}{225}=1$

∴ The equation of the ellipse is $\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1$

6 0

4 years ago

A small junior college had an enrollment of 7,843 students in the year 1990 and 8,793 students in the year 2000. Let x=0 represe

abruzzese [7]

Correct answer is: (0,7843) and (10,8793)

Solution:-

Given that a junior college has an enrollment of 7843 students in 1990 and 8793 students in year 2000.

We have to write this data as (x,y) .

Where x= years after 1990 and y=number of students enrolled.

Since in 1990, 7843 students enrolled, x = 1990-1990=0

And y=7843.

Hence one ordered pair is (0,7843).

Let us find the years after 1990 for 2000 = 2000-1990 =10

Hence another ordered pair is (10,8793).

4 0

4 years ago

40 POINTS!!!!!!!! NEED HELP

aniked [119]

Where is the grid are u gonna take a pic?

6 0

3 years ago

The vertex of the function’s graph is given. Find c. y = x2 + 10x + c; (-5, -27)

castortr0y [4]

Actually I didn't see the (-5, -27), the answer would be -2.

5 0

3 years ago

32x - 4 = 4x2 + 60 For the equation shown, choose the description of the solutions.

Furkat [3]

All to one side:

4x^2-32x+64 = 0,

divide by 4:

x^2 -8x + 16 = 0

apply formula or see that it is (x-4)^2!, so only x =4 is a root and it is double.

3 0

3 years ago

Read 2 more answers