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3 years ago

A third line goes through the same point. How would that show up in a table representing the relationship for the third line?

Mathematics

1 answer:

romanna [79]3 years ago

7 0

Answer:

Most likely the table will contain one pair of values that correspond to the coordinate where the previous lines intersect.

Step-by-step explanation:

It may be possible that the table before the third line contains values on either side of the point of intersection, but the slope will produce a line that connects those values and passes through the previous intersection.

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The equation for the ellipse given is 4x^2+9y^2-16x+18y-11

natita [175]

Answer:

a. a = 3, b = 2

b. The coordinate of the center is (2, -1)

c. The eccentricity of the ellipse is √5/3

d. Please see attached graph of the ellipse created with MS Excel

Step-by-step explanation:

7. a. The given equation of the ellipse is presented as follows;

4·x² + 9·y² - 16·x + 18·y - 11

The general equation of an ellipse

$\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1$

We can write;

4·x² - 16·x + 9·y² + 18·y - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) - 25 - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) = 25 + 11 = 36

4·(x - 2)² + 9·(y + 1)² = 36

$\dfrac{4\cdot (x - 2)^2}{36} + \dfrac{9 \cdot (y + 1)^2}{36} = \dfrac{36}{36}$

$\therefore \dfrac{ (x - 2)^2}{9} + \dfrac{ (y + 1)^2}{4} = \dfrac{ (x - 2)^2}{3^2} + \dfrac{ (y + 1)^2}{2^2} = 1$

By comparison, a = 3, b = 2, h = 2, k = -1

b. The coordinate of the center, (h, k) = (2, -1)

c. The eccentricity of the ellipse = c/a

c² = a² - b²

∴ c² = 3² - 2² = 5

c = √5

Eccentricity = √5/3

d. Please find attached the graph of the ellipse created with MS Excel

8 0

3 years ago

To derive the standard formula of a circle, a radius r is constructed as the hypotenuse of a right triangle as shown. On a coord

vlabodo [156]

Answer:

The answer is "x-h and y-k".

Step-by-step explanation:

The center is (h, k) with E (x, y) point, and its length of the legs used during extracting the standard circle equation should be found. Its right triangle length base is (x-h) units, as well as the right triangle's length, is (y-k). So, these are the required leg lengths, that's why the above-given points are correct.

4 0

3 years ago

Which of the following are trigonometric identities? Check all that apply.

lubasha [3.4K]

Answer:

C and D is correct

That's what I think though

3 0

3 years ago

Help me pleaseeeeeeee

kirill115 [55]

Step-by-step explanation: