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Question 29 Find the standard form...

Question 29

Find the standard form of the equation of the ellipse satisfying the given conditions.

Endpoints of major axis: (7, 9) and (7, 3)

Endpoints of minor axis: (5, 6) and (9, 6)

A. (x - 7)2/6 + (y - 6)2/7 = 1

B. (x - 7)2/5 + (y - 6)2/6 = 1

C. (x - 7)2/4 + (y - 6)2/9 = 1

D. (x - 5)2/4 + (y - 4)2/9 = 1

Question 30

Convert each equation to standard form by completing the square on x and y.

9x2 + 16y2 - 18x + 64y - 71 = 0

A. (x - 1)2/9 + (y + 2)2/18 = 1

B. (x - 1)2/18 + (y + 2)2/71 = 1

C. (x - 1)2/16 + (y + 2)2/9 = 1

D. (x - 1)2/64 + (y + 2)2/9 = 1

Question 31

Locate the foci of the ellipse of the following equation.

25x2 + 4y2 = 100

A. Foci at (1, -√11) and (1, √11)

B. Foci at (0, -√25) and (0, √25)

C. Foci at (0, -√22) and (0, √22)

D. Foci at (0, -√21) and (0, √21)

Question 32

Locate the foci of the ellipse of the following equation.

7x2 = 35 - 5y2

A. Foci at (0, -√2) and (0, √2)

B. Foci at (0, -√1) and (0, √1)

C. Foci at (0, -√7) and (0, √7)

D. Foci at (0, -√5) and (0, √5)

Question 33

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (0, -4), (0, 4)

Vertices: (0, -7), (0, 7)

A. x2/43 + y2/28 = 1

B. x2/33 + y2/49 = 1

C. x2/53 + y2/21 = 1

D. x2/13 + y2/39 = 1

Question 34

Convert each equation to standard form by completing the square on x and y.

9x2 + 25y2 - 36x + 50y - 164 = 0

A. (x - 2)2/25 + (y + 1)2/9 = 1

B. (x - 2)2/24 + (y + 1)2/36 = 1

C. (x - 2)2/35 + (y + 1)2/25 = 1

D. (x - 2)2/22 + (y + 1)2/50 = 1

Question 35

Find the solution set for each system by finding points of intersection.

x2 + y2 = 1

x2 + 9y = 9

A. {(0, -2), (0, 4)}

B. {(0, -2), (0, 1)}

C. {(0, -3), (0, 1)}

D. {(0, -1), (0, 1)}

Question 36

Locate the foci and find the equations of the asymptotes.

4y2 – x2 = 1

A. (0, ±√4/2); asymptotes: y = ±1/3x

B. (0, ±√5/2); asymptotes: y = ±1/2x

C. (0, ±√5/4); asymptotes: y = ±1/3x

D. (0, ±√5/3); asymptotes: y = ±1/2x

Question 38

Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.

y2 - 2y + 12x - 35 = 0

A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9

B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6

C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6

D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus (0, 1); directrix: x = 8

Question 40 Locate the foci of the ellipse of the following equation.

x2/16 + y2/4 = 1

A. Foci at (-2√3, 0) and (2√3, 0)

B. Foci at (5√3, 0) and (2√3, 0)

C. Foci at (-2√3, 0) and (5√3, 0)

D. Foci at (-7√2, 0) and (5√2, 0)

a. Use the numbers shown in the bar graph below to find the total cost of tuition and fees at public colleges for a four year period from the school year ending in 2007 through the school year ending in 2010.

b. The model an = 395n + 5419 describes the cost of tuition and fees at public colleges in academic year n, where n = 1 corresponds to the school year ending in 2007, n = 2 to the school year ending in 2008, and so on.

1) Use this model and the formula for Sn to find the total cost of tuition and fees at public colleges for a four-year period from the school year ending in 2007 through the school year ending in 2010.

2) How does this compare with the actual sum you obtained in part (a)?

Find the standard form of the equation of the ellipse satisfying the given conditions.

Endpoints of major axis: (7, 9) and (7, 3)

Endpoints of minor axis: (5, 6) and (9, 6)

A. (x - 7)2/6 + (y - 6)2/7 = 1

B. (x - 7)2/5 + (y - 6)2/6 = 1

C. (x - 7)2/4 + (y - 6)2/9 = 1

D. (x - 5)2/4 + (y - 4)2/9 = 1

Question 30

Convert each equation to standard form by completing the square on x and y.

9x2 + 16y2 - 18x + 64y - 71 = 0

A. (x - 1)2/9 + (y + 2)2/18 = 1

B. (x - 1)2/18 + (y + 2)2/71 = 1

C. (x - 1)2/16 + (y + 2)2/9 = 1

D. (x - 1)2/64 + (y + 2)2/9 = 1

Question 31

Locate the foci of the ellipse of the following equation.

25x2 + 4y2 = 100

A. Foci at (1, -√11) and (1, √11)

B. Foci at (0, -√25) and (0, √25)

C. Foci at (0, -√22) and (0, √22)

D. Foci at (0, -√21) and (0, √21)

Question 32

Locate the foci of the ellipse of the following equation.

7x2 = 35 - 5y2

A. Foci at (0, -√2) and (0, √2)

B. Foci at (0, -√1) and (0, √1)

C. Foci at (0, -√7) and (0, √7)

D. Foci at (0, -√5) and (0, √5)

Question 33

Find the standard form of the equation of the following ellipse satisfying the given conditions.

Foci: (0, -4), (0, 4)

Vertices: (0, -7), (0, 7)

A. x2/43 + y2/28 = 1

B. x2/33 + y2/49 = 1

C. x2/53 + y2/21 = 1

D. x2/13 + y2/39 = 1

Question 34

Convert each equation to standard form by completing the square on x and y.

9x2 + 25y2 - 36x + 50y - 164 = 0

A. (x - 2)2/25 + (y + 1)2/9 = 1

B. (x - 2)2/24 + (y + 1)2/36 = 1

C. (x - 2)2/35 + (y + 1)2/25 = 1

D. (x - 2)2/22 + (y + 1)2/50 = 1

Question 35

Find the solution set for each system by finding points of intersection.

x2 + y2 = 1

x2 + 9y = 9

A. {(0, -2), (0, 4)}

B. {(0, -2), (0, 1)}

C. {(0, -3), (0, 1)}

D. {(0, -1), (0, 1)}

Question 36

Locate the foci and find the equations of the asymptotes.

4y2 – x2 = 1

A. (0, ±√4/2); asymptotes: y = ±1/3x

B. (0, ±√5/2); asymptotes: y = ±1/2x

C. (0, ±√5/4); asymptotes: y = ±1/3x

D. (0, ±√5/3); asymptotes: y = ±1/2x

Question 38

Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.

y2 - 2y + 12x - 35 = 0

A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9

B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6

C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6

D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus (0, 1); directrix: x = 8

Question 40 Locate the foci of the ellipse of the following equation.

x2/16 + y2/4 = 1

A. Foci at (-2√3, 0) and (2√3, 0)

B. Foci at (5√3, 0) and (2√3, 0)

C. Foci at (-2√3, 0) and (5√3, 0)

D. Foci at (-7√2, 0) and (5√2, 0)

a. Use the numbers shown in the bar graph below to find the total cost of tuition and fees at public colleges for a four year period from the school year ending in 2007 through the school year ending in 2010.

b. The model an = 395n + 5419 describes the cost of tuition and fees at public colleges in academic year n, where n = 1 corresponds to the school year ending in 2007, n = 2 to the school year ending in 2008, and so on.

1) Use this model and the formula for Sn to find the total cost of tuition and fees at public colleges for a four-year period from the school year ending in 2007 through the school year ending in 2010.

2) How does this compare with the actual sum you obtained in part (a)?

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