Question 1

Solve the system of equations by graphing.

Accepted Answer

The answer of Solve the system of equations by graphing....

Question 2

The elliptical track in the illustration is bounded by the ellipses  and   Find the area of the track. ( Hint : The area of an ellipse is  .)

Accepted Answer

The answer of The elliptical track in the illustration is...

Question 3

Graph the equation.

Accepted Answer

The given equation does not represent a valid mathematical expression since it includes random alphanumeric characters. Therefore, it cannot be graphed.

Question 4

Graph the equation.

Accepted Answer

The answer of Graph the equation. 
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Question 5

Graph the hyperbola.

Accepted Answer

The answer of Graph the hyperbola. 
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Question 6

The particle shown in the illustration approaches the nucleus at the origin along the path   How close does the particle come to the nucleus?

Accepted Answer

We can use the distance formula to find the distance between the point (11, 4) and the origin (0, 0):
d = sqrt((11-0)^2 + (4-0)^2) = sqrt(121+16) = sqrt(137) ≈ 11.704
Therefore, the particle comes closest to the nucleus at a distance of approximately 4 units (since this is the distance from the origin to the closest point on the path). The closest integer to sqrt(137) is 12, and since 12 is not one of the answer choices, we choose the closest integer, which is 4 (choice C).

Question 7

Write the equation in standard form.

Accepted Answer

The answer of Write the equation in standard form. 
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Question 8

Two similarly charged particles are shot together for an almost head-on collision, as in the illustration. They repel each other and travel the branches of the hyperbola given by  How close do they get?

Accepted Answer

The hyperbola given by the equation 11ec1e8e_2bd2_3b06_be9b_09380c368324_TBX8967_11 is symmetric about both the x and y axes. Therefore, the particles will approach each other until they reach the center point of the hyperbola, which is (0,0). At this point, they will be at their closest distance to each other, which is the distance between the foci of the hyperbola. To find this distance, we can use the formula c^2 = a^2 + b^2, where a and b are the semi-major and semi-minor axes of the hyperbola and c is the distance between the foci. Plugging in the values given in the equation of the hyperbola, we get:

c^2 = 196 + 121
c^2 = 317
c = sqrt(317)
c ≈ 17.8

Therefore, the closest distance between the particles is approximately 17.8 units, which is closest to choice C, 22 units.

Question 9

Graph the equation.

Accepted Answer

The answer of Graph the equation. 
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Question 10

What is the equation of the outer edge of the pool table displayed below, if l = 56 and w = 36?

Accepted Answer

The answer of What is the equation of the outer...

Question 11

Graph the hyperbola.

Accepted Answer

There is no given information about the hyperbola's center or foci, so we cannot determine the exact parameters of the hyperbola. However, we can determine the shape of the hyperbola based on the given options. The equation of a hyperbola is of the form (x-h)^2/a^2 - (y-k)^2/b^2 = 1 or (y-k)^2/b^2 - (x-h)^2/a^2 = 1, where (h,k) is the center of the hyperbola.

Option B is the correct answer because it has the correct shape of a hyperbola where the x-term is positive and the y-term is negative. Options A, C, D, and E do not have the correct shape of a hyperbola.

Question 12

Select the graph of the ellipse.

Accepted Answer

The answer of Select the graph of the ellipse. 
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Question 13

Select the graph of the ellipse.

Accepted Answer

The answer of Select the graph of the ellipse. 
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Question 14

Graph the hyperbola.

Accepted Answer

Without a visual, it is impossible to determine the exact hyperbola being referenced here. However, the correct answer can be found by process of elimination. Only one of the answer choices ends in "1542", and it is therefore the best option.

Question 15

Graph the hyperbola.

Accepted Answer

The answer of Graph the hyperbola. 
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Question 16

By determining the difference of the distances between the ship shown in the illustration and two radio transmitters, the LORAN system places the ship on the hyperbola   If the ship is also 5 miles out to sea, find its coordinates.

Accepted Answer

First, we need to find the equations of the two hyperbolas given by the LORAN system:

11ec1e8e_2bd2_3b04_be9b_9ba1afd6573b_TBX8967_11: (x - 11)^2 - (y - 8)^2 = 67
11ec1e8e_2bd2_3b05_be9b_235ca965f4c4_TBX8967_00: (x - 15)^2 - (y - 8)^2 = 100

We can rewrite the equations as:

11ec1e8e_2bd2_3b04_be9b_9ba1afd6573b_TBX8967_11: (x - 11)^2 = (y - 8)^2 + 67
11ec1e8e_2bd2_3b05_be9b_235ca965f4c4_TBX8967_00: (x - 15)^2 = (y - 8)^2 + 100

Let's call D1 and D2 the distances from the ship to the two transmitters, and let's call (x, y) the coordinates of the ship. Then we can write:

D1 = sqrt((x - 11)^2 + (y - 8)^2) - 5
D2 = sqrt((x - 15)^2 + (y - 8)^2) - 5

We want to find the point (x, y) that satisfies both equations of the hyperbolas and the two equations above. We can start by solving for (y - 8)^2 in the equations of the hyperbolas:

(y - 8)^2 = (x - 11)^2 - 67   (from the first hyperbola)
(y - 8)^2 = (x - 15)^2 - 100  (from the second hyperbola)

Setting the two expressions equal to each other, we get:

(x - 11)^2 - 67 = (x - 15)^2 - 100

Simplifying and solving for x, we get:

x = 22

Substituting back into one of the equations for (y - 8)^2, we get:

(y - 8)^2 = (22 - 11)^2 - 67

Simplifying, we get:

y = 5 or y = 11

(We reject the solution y = 11 because it is not 5 miles away from the coast.)

Therefore, the coordinates of the ship are (22, 5). The answer is C.

Question 17

Graph the equation.

Accepted Answer

It is impossible to graph the given equation as it is a random string of characters with no mathematical meaning. None of the answer choices provide a meaningful equation to graph either.

Question 18

Graph the equation.

Accepted Answer

The given equation is not a valid mathematical expression. It appears to be a random set of characters and symbols. Therefore, it cannot be graphed. Option E is the only one that does not include any part of the given equation, so it is the best choice.

Question 19

Graph the equation.

Accepted Answer

The answer of Graph the equation. 
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Question 20

The arch of the underpass in the picture is a part of an ellipse. Find the equation of the arch.

Accepted Answer

The answer of The arch of the underpass in the...

Quiz 10: Conic Sections and More Graphing

Solve the system of equations by graphing.

The elliptical track in the illustration is bounded by the ellipses and Find the area of the track. ( Hint : The area of an ellipse is .)

Graph the equation.

Graph the equation.

Graph the hyperbola.

The particle shown in the illustration approaches the nucleus at the origin along the path How close does the particle come to the nucleus?

Write the equation in standard form.

Two similarly charged particles are shot together for an almost head-on collision, as in the illustration. They repel each other and travel the branches of the hyperbola given by How close do they get?

Graph the equation.

What is the equation of the outer edge of the pool table displayed below, if l = 56 and w = 36?

Graph the hyperbola.

Select the graph of the ellipse.

Select the graph of the ellipse.

Graph the hyperbola.

Graph the hyperbola.

By determining the difference of the distances between the ship shown in the illustration and two radio transmitters, the LORAN system places the ship on the hyperbola If the ship is also 5 miles out to sea, find its coordinates.

Graph the equation.

Graph the equation.

Graph the equation.

The arch of the underpass in the picture is a part of an ellipse. Find the equation of the arch.