Answers LAUSD-Algebra II B Prescriptive - SummerEquations of Ellipses

Unit Test Answers

0 verified answers

Free Preview

Question text not available

points G and H

points J and K

points L and N

points M and N

Free Preview

The center of a hyperbola is located at the origin. One focus is located at (0, 20), and its associated directrix is represented by the line y = . What is the equation of the hyperbola?

= 1

= 1

= 1

= 1

Which of the following represents the measures of all angles coterminal with a 418° angle?

360 + 58n, for any whole number n

58 + 360n, for any integer n

58 + 360n, for any whole number n

360 + 58n, for any integer n

If , which of the following represents approximate values of and , for ?

sine theta almost-equals 0.9511; tangent theta almost equals 0.3249

sine theta almost-equals 0.9511; tangent theta almost equals 3.0780

sine theta almost-equals 3.2362; tangent theta almost-equals 0.0955

sine theta almost-equals 3.2362; tangent theta almost-equals 10.4731

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units.The center of the circle lies on the x-axis.The center of the circle lies on the y-axis.The standard form of the equation is (x – 1)² + y² = 3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The radius of the circle is 3 units.

The center of the circle lies on the x-axis.

The center of the circle lies on the y-axis.

The standard form of the equation is (x – 1)² + y² = 3.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

An ellipse has vertices along the major axis at (0, 1) and (0, −9). The foci of the ellipse are located at (0, −1) and (0, −7). The equation of the ellipse is in the form below.

a = 10

b = 4

h = 3

k = 0

Which equation represents a hyperbola with a center at (0, 0), a vertex at (−48, 0), and a focus at (50, 0)?

= 1

What is the equation of the graph below?

y = sine (x + 90 degrees)

y = cosine (x + 90 degrees)

y = sine (x + 45 degrees)

y = cosine (x + 45 degrees)

Which of the following is the equation of the function below?

y equal to 2 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.

y equal to 2 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) minus 1 right-square-bracket.

y equal to 0 point 5 cosecant left-square-bracket 0 point 5 (x plus StartFraction pi over 2 EndFraction) right-square-bracket minus 1.

y equal to 0 point 5 cosecant left-square-bracket 2 (x plus StartFraction pi over 4 EndFraction) right-square-bracket minus 1.

How does the graph of y = sec(x + 3) – 7 compare with the graph of y = sec(x)?

It is the graph of y = sec(x) shifted 3 units right and 7 units up.

It is the graph of y = sec(x) shifted 3 units left and 7 units up.

It is the graph of y = sec(x) shifted 3 units left and 7 units down.

It is the graph of y = sec(x) shifted 3 units right and 7 units down.

What is 270° converted to radians?

StartFraction pi Over 6 EndFraction

StartFraction 3 Over 2 EndFraction

StartFraction 3 pi Over 2 EndFraction

What is the range of y = –3sin(x) – 4?

all real numbers

A point is on a circle if the distance from the center of the circle to the point is equal to the

area.

circumference.

radius.

diameter.

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when and that the windmill turns counterclockwise at a constant rate.

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30

y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10

y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30

Which of the following could be the equation of the function below?

y = negative 3 sine (2 (x + pi)) + 2

y = negative 3 sine (x + pi) + 2

y = 3 sine (4 (x minus pi)) + 4

y = 3 sine (2 (x + pi)) + 2

What are the values of m and in the diagram below?

Which transformation should be applied to the graph of the function to obtain the graph of the function ?

a vertical stretch, a horizontal compression to make the period , a horizontal shift of units to the right, and a vertical shift of 4 units up

Which of the following is true of the location of an angle, , whose tangent value is ?

has a 30-degree reference angle and is located in Quadrant II or IV

has a 30-degree reference angle and is located in Quadrant II or III

has a 60-degree reference angle and is located in Quadrant II or IV

has a 60-degree reference angle and is located in Quadrant II or III

Three trigonometric functions for a given angle are shown below.What are the coordinates of point (x, y) on the terminal ray of angle , assuming that the values above were not simplified?

(–5, 12)

(5, –12)

(–12, 5)

(12, –5)

Which function will have a y-intercept at –1 and an amplitude of 2?

f (x) = negative sine (X) minus 1

f (x) = negative 2 sine (x) minus 1

f (x) = negative cosine (x)

f (x) = negative 2 cosine (x) minus 1

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth.

0.4 radian

1.0 radian

2.7 radians

5.0 radians

Which is an x-intercept of the graph of the function ?

(minus StartFraction 2pi over 3 EndFraction , 0)

(minus StartFraction pi over 3 EndFraction , 0)

(StartFraction pi over 6 EndFraction , 0)

(StartFraction 5pi over 6 EndFraction , 0)

An angle measuring (468n)° is in standard position. For which value of n will the terminal side fall on the x-axis?

n = 4

n = 5

n = 6

n = 7

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5