Mathematics: B What is the center, major axis and vertices

B What is the center, major axis and vertices, №14458114, 10.12.2020 14:52

Mathematics

8.08, part 1 1. find the vertex, focus, directrix, and focal width of the parabola. negative 1 divided by 16 times x squared = y a) vertex: (0, 0); focus: (0, -4); directrix: y = 4; focal width: 16 b) vertex: (0, 0); focus: (-8, 0); directrix: x = 4; focal width: 64 c) vertex: (0, 0); focus: (0, 4); directrix: y = -4; focal width: 4 d) vertex: (0, 0); focus: (0, -4); directrix: y = 4; focal width: 64 2. find the standard form of the equation of the parabola with a focus at (0, -8) and a directrix at y = 8. a) y = negative 1 divided by 32 x2 b)

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P Answered by Specialist

Hello,
Please, see the detailed solutions in the attached files.
Thanks.

8.08, part 1 1. find the vertex, focus, directrix, and focal width of the parabola. negative 1 divi

Mathematics

8.08, part 1 1. find the vertex, focus, directrix, and focal width of the parabola. negative 1 divided by 16 times x squared = y a) vertex: (0, 0); focus: (0, -4); directrix: y = 4; focal width: 16 b) vertex: (0, 0); focus: (-8, 0); directrix: x = 4; focal width: 64 c) vertex: (0, 0); focus: (0, 4); directrix: y = -4; focal width: 4 d) vertex: (0, 0); focus: (0, -4); directrix: y = 4; focal width: 64 2. find the standard form of the equation of the parabola with a focus at (0, -8) and a directrix at y = 8. a) y = negative 1 divided by 32 x2 b)

Step-by-step answer

P Answered by Master

Hello,
Please, see the detailed solutions in the attached files.
Thanks.

Mathematics

Which of the following statements is a fact about ellipses? choose the correct statement below. a. the square of the length of the major axis is equal to the difference between the square of the length of the minor axis and the square of the distance from the center of the ellipse to a focus. b. the sum of the squares of the distances between the two foci and the center is equal to the square of the length of the minor axis. c. the square of half the length of the minor axis is equal to the difference between the square of half the length of the

Step-by-step answer

P Answered by PhD

2

C

Step-by-step explanation:

The distance from the focus to the co-vertex is the length of the semi-major axis. Expressed in terms of the Pythagorean theorem, that relationship matches the description in selection C:

The square of the semi-minor axis is equal the the difference between the square of the semi-major axis and the square of the distance from the center to a focus.
Which of the following statements is a fact about ellipses? choose the correct statement below. a.

Mathematics

Which of the following statements is a fact about ellipses? choose the correct statement below. a. the square of the length of the major axis is equal to the difference between the square of the length of the minor axis and the square of the distance from the center of the ellipse to a focus. b. the sum of the squares of the distances between the two foci and the center is equal to the square of the length of the minor axis. c. the square of half the length of the minor axis is equal to the difference between the square of half the length of the

Step-by-step answer

P Answered by PhD

2

C

Step-by-step explanation:

The distance from the focus to the co-vertex is the length of the semi-major axis. Expressed in terms of the Pythagorean theorem, that relationship matches the description in selection C:

The square of the semi-minor axis is equal the the difference between the square of the semi-major axis and the square of the distance from the center to a focus.
Which of the following statements is a fact about ellipses? choose the correct statement below. a.

Mathematics

The planets in our solar system do not travel in circular paths. Rather, their orbits are elliptical. The Sun is located at a focus of the ellipse. The perihelion is the point in a planet’s orbit that is closest to the Sun. So, it is the endpoint of the major axis that is closest to the Sun. The aphelion is the point in the planet’s orbit that is furthest from the Sun. So, it is the endpoint of the major axis that is furthest from the Sun. The closest Mercury comes to the Sun is about 46 million miles. The farthest Mercury travels from the Sun

Step-by-step answer

P Answered by Specialist

1

(1) 83.764 million miles

(2) 52.766 million miles

(3) $\frac{x^2}{4900}+\frac{y^2}{2116}=1.$

Step-by-step explanation:

Let the origin C(0,0) be the center of the elliptical path as shown in the figure, where the location of the sun is at one of the two foci, say f.

The standard equation of the ellipse having the center at the origin is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\;\cdots(i)$

where and are the semi-axes of the ellipse along the x-axis and y-axis respectively.

Let the points P and A represent the points of perihelion (nearest to the sun) and the aphelion (farthest to the sun) of the closest planet Mercury.

Given that,

CP=46 million miles and

CA=70 million miles.

So, CP=b is the semi-minor axis and CA=a is the semi-major axis.

Let the distances on the axes are in millions of miles. So, the coordinates of the point P and A are P(0,46) and A(70,0) respectively.

(1) From the distance formula, the distance between the perihelion and the aphelion is

$PA=\sqrt{(0-70)^2+(46-0)^2}=83.764$ million miles.

(2) Location of the Sun is at focus, , of the elliptical path.

From the standard relation, the distance of the focus from the center of the ellipse, c, is

$c=ae\;\cdots(ii)$

where and are the semi-major axis and the eccentricity of the ellipse.

The eccentricity of the ellipse is

$e=\sqrt{1-\frac{b^2}{a^2}}$

$\Rightarrow e=\sqrt{1-\frac{46^2}{70^2}}=0.7538$ .

Hence, from the equation (i) the distance of the Sun from the center of the elliptical path of the Mercury is

$c=70\times0.7538=52.766$ million miles.

(3) From the equation (i), the equation of the elliptical orbit of Mercury is

$\frac{x^2}{70^2}+\frac{46^2}{b^2}=1$

$\Rightarrow \frac{x^2}{4900}+\frac{y^2}{2116}=1.$

The planets in our solar system do not travel in circular paths. Rather, their orbits are elliptical

Mathematics

A designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 40 meters, which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guests to stand to experience his whisper chamber will be 5 meters from the center of the warehouse space, which will act as the foci. How far out from the center, along the minor axis, should he build his whisper chamber? A: 19.4 m B: 38.7 m C: 39.7 m D: 79.4 m

Step-by-step answer

P Answered by Specialist

15

the answer is 19.4m

Step-by-step explanation:

Mathematics

A designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 40 meters, which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guests to stand to experience his whisper chamber will be 5 meters from the center of the warehouse space, which will act as the foci. How far out from the center, along the minor axis, should he build his whisper chamber? A: 19.4 m B: 38.7 m C: 39.7 m D: 79.4 m

Step-by-step answer

P Answered by Specialist

15

the answer is 19.4m

Step-by-step explanation:

Mathematics

write the equation for the conic section if the cone is centered at (0,0), the major axis is 10 units, and the minor axis is 6 units. (there is more than one correct answer.) teach said because it didn t want one over the other that we could pick one. i picked the horizontal form. (x^2/a^2)+(y^2/b^2)=1 i stuck the major in for a and the minor for b, so what do i do next?

Step-by-step answer

P Answered by PhD

This conic section is an ellipse.
Here: 2a = 10 ( the major axis ) and 2 b = 6 ( the minor axis );
and the formula is:
x² / a² + y² / b² = 1
So: a = 10 : 2 = 5 and b = 6 : 2 = 3.
x² / 5² + y² / 3² = 1

The equation is: x² / 25 + y² / 9 = 1.

Mathematics

write the equation for the conic section if the cone is centered at (0,0), the major axis is 10 units, and the minor axis is 6 units. (there is more than one correct answer.) teach said because it didn t want one over the other that we could pick one. i picked the horizontal form. (x^2/a^2)+(y^2/b^2)=1 i stuck the major in for a and the minor for b, so what do i do next?

Step-by-step answer

P Answered by PhD

This conic section is an ellipse.
Here: 2a = 10 ( the major axis ) and 2 b = 6 ( the minor axis );
and the formula is:
x² / a² + y² / b² = 1
So: a = 10 : 2 = 5 and b = 6 : 2 = 3.
x² / 5² + y² / 3² = 1

The equation is: x² / 25 + y² / 9 = 1.

Mathematics

The equation for an ellipse with a horizontal major axis is x²/a² +y²/b² =1 . the orbit for mercury can be plotted on the coordinate plane with the center at the origin and the sun located at one focus. use this information and the mercury’s calculated mean distance from the sun to find the value of a. express your answer in millions of miles

Step-by-step answer

P Answered by Specialist

Mercury's mean distance from the sun = 35,983,000 miles

(planet)

The equation for an ellipse with a horizontal major axis is x²/a² +y²/b² =1 . the orbit for mercury

The equation for an ellipse with a horizontal major axis is x²/a² +y²/b² =1 . the orbit for mercury

B
What is the center, major axis and vertices

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