Answers PrecalculusEquations of Ellipses

Equations of Ellipses — Unit test Answers

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A student uses the equation to represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline , where . To solve the problem, the student used the given value of to find the value of and then substituted the value of in the equation above to solve for s. What is the approximate value of s, the speed of the car in feet per second?

5.3

7.5

9.2

28.3

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An ellipse has a center at the origin, a vertex along the major axis at (20, 0), and a focus at (16, 0). The equation of the ellipse is in the form below.

Which statement accurately describes how adding a number, n, to the function affects its graph?

There is a vertical shift of n units.

The x-intercepts will shift n units.

There is a change in amplitude of n units.

The range will change by a factor of 2n units.

What is the radius of a circle whose equation is x2+y2+8x−6y+21=0?

2 units

3 units

4 units

5 units

An angle measuring (870n)° is in standard position. For which value of n will the terminal side fall on the y-axis?

n = 3

n = 4

n = 5

n = 6

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3.25 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8.75 meters. Which of the following equations models d, the depth of the water in meters, as a function of time, t, in hours? Let t = 0 be 12:00 a.m.

d = negative 3.75 cosine (StartFraction 4 pi Over 31 EndFraction t) + 5

d = negative 3.75 cosine (StartFraction 4 pi Over 29 EndFraction t) + 5

d = negative 2.75 cosine (StartFraction 4 pi Over 31 EndFraction t) + 6

d = negative 2.75 cosine (StartFraction 4 pi Over 29 EndFraction t) + 6

Which of the following is the graph of ?

On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at pi.

On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 1 cycle at 2 pi.

On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.

On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.

What is the domain of the function ?

all real numbers except , where n is any integer

Henry is asked to find the exact value of . His steps are shown below.1. Subtract from as many times as possible: – = 2. Find the reference angle for : – = .3. The cosine value for is .4. The cosine value is positive because is in the first quadrant.Which of the following describes Henry’s errors?

The reference angle should be , and the sign of the value should be negative.

The reference angle should be , and the cosine value for is .

The sign of the value should be negative, and the reference angle and quadrant should be determined by subtracting in the first step.

The cosine value for is , and the reference angle and quadrant should be determined by subtracting in the first step.

Which of the following represents the measures of all angles coterminal with a –220° angle?

360 + 140n, for any whole number n

360 + 140n, for any integer n

140+ 360n, for any whole number n

140 + 360n, for any integer n

A circle has a central angle measuring radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for .

3.7 cm

4.9 cm

14.3 cm

15.4 cm

On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal distance from the y-axis to the same point. What is sin?