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College Algebra 7th Edition Robert F Blitzer - Solutions
In Exercises 1–8, graph each ellipse and locate the foci.9x2 + 4y2 - 18x + 8y - 23 = 0
In Exercises 6–11, graph each hyperbola. Give the location of the foci and the equations of the asymptotes.y2 - 4x2 = 16
Fill in each blank so that the resulting statement is true.In the equation 3(x2 + 4x) + 4(y2 - 2y) = 32, we complete the square on x by adding________ within the first parentheses. We complete the square on y by adding_________ within the second parentheses. Thus, we must add_________ to the right
In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions.Foci: (-7, 0), (7, 0); vertices: (-5, 0), (5, 0)
Identify the conic represented by x2 + 9y2 + 10x - 18y + 25 = 0 without completing the square.
Find the sum of the first ten terms of the sequence:5, 10, 20, 40, . . . .
Fill in each blank so that the resulting statement is true.If the center of a hyperbola with a horizontal transverse axis is (2, 3) and a2 = 25, then the coordinates of the vertices are______ and________ .
Solve each system in Exercises 8–10.(Use matrices.) x = y + z y + z = 17 -4x + y + 5z = -2 2x + 3y + z 8
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.x2 = 12y
Fill in each blank so that the resulting statement is true.The center of= 1 is_______ . (y + 2)² 4 (x-7)² 36
In Exercises 1–18, graph each ellipse and locate the foci. x o 25 4 1
Fill in each blank so that the resulting statement is true.If 4p = 4, then the length of the latus rectum is_________ . The endpoints of the latus rectum are________ and__________ . (-2,-1)
A sound whispered at one focus of a whispering gallery can be heard at the other focus. The figure shows a whispering gallery whose cross section is a semielliptical arch with a height of 24 feet and a width of 80 feet. How far from the room’s center should two people stand so that they can
In Exercises 9–11, find the standard form of the equation of each ellipse satisfying the given conditions.Foci: (-4, 0), (4, 0); Vertices: (-5, 0), (5, 0)
In Exercises 6–11, graph each hyperbola. Give the location of the foci and the equations of the asymptotes. (x - 2)² (y + 2)² 9 16 = 1
In Exercises 6–11, graph each hyperbola. Give the location of the foci and the equations of the asymptotes.4x2 - 49y2 = 196
In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions.Endpoints of transverse axis: (0, -6), (0, 6); asymptote: y = 2x
An engineer is designing headlight units for cars. The unit shown in the figure has a parabolic surface with a diameter of 6 inches and a depth of 3 inches.a. Using the coordinate system that has been positioned on the unit, find the parabola’s equation.b. If the light source is located at the
In Exercises 1–18, graph each ellipse and locate the foci. 2 X 81 25 16 = 1
Find the sum of the first 50 terms of the sequence:-2, 0, 2, 4, . . . .
Find the sum of the first ten terms of the sequence:-20, 40, -80, 160, . . . .
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.x2 = 8y
In Exercises 9–11, find the standard form of the equation of each ellipse satisfying the given conditions.Foci: (0, -3), (0, 3); Vertices: (0, -6), (0, 6)
In Exercises 12–15, find each indicated sum. 4 Σ ( + 4)(i – 1) i=1
Fill in each blank so that the resulting statement is true.In the equation 9(x2 - 8x) - 16(y2 + 2y) = 16, we complete the square on x by adding______ within the first parentheses. We complete the square on y by adding______ within the second parentheses. Thus, we must add_______ to the right side
In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions.Endpoints of transverse axis: (-4, 0), (4, 0); asymptote: y = 2x
Find the sum of the first 100 terms of the sequence:4, -2, -8, -14, . . . .
In Exercises 11–13, graph each equation, function, or system in a rectangular coordinate system. X 9 4 = 1
In Exercises 11–13, graph each equation, function, or system in a rectangular coordinate system.f(x) = (x - 1)2 - 4
In Exercises 6–11, graph each hyperbola. Give the location of the foci and the equations of the asymptotes.4x2 - y2 + 8x + 6y + 11 = 0
Fill in each blank so that the resulting statement is true.A nondegenerate conic section in the form Ax2 + Cy2 + Dx + Ey + F = 0, in which A and C are not both zero is a/an_________ if A = C, a/an________ if AC = 0, a/an__________ if A ≠ C and AC > 0, and a/an______ if AC < 0.
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.x2 = -16y
In Exercises 9–11, find the standard form of the equation of each ellipse satisfying the given conditions.Major axis horizontal with length 12; length of minor axis = 4; center: (-3, 5)
In Exercises 1–18, graph each ellipse and locate the foci.x2 = 1 - 4y2
In Exercises 5–12, find the standard form of the equation of each hyperbola satisfying the given conditions.Center: (4, -2); Focus: (7, -2); vertex: (6, -2)
In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.x2 = -20y
A semielliptical arch supports a bridge that spans a river 20 yards wide. The center of the arch is 6 yards above the river’s center. Write an equation for the ellipse so that the x-axis coincides with the water level and the y-axis passes through the center of the arch. PAPA 16 yd 20 yd-
Use the matrix feature of a graphing utility to verify each of your answers to Exercises 37–44.Data from Exercise 37-44 In Exercises 37-44, perform the indicated matrix operations given that A, B, and C are defined as follows. If an operation is not defined, state the reason. A = 40 -3 5 01 37.
In Exercises 77–78, use a coding matrix A of your choice. Use a graphing utility to find the multiplicative inverse of your coding matrix. Write a cryptogram for each message. Check your result by decoding the cryptogram. Use your graphing utility to perform all necessary matrix multiplications.
The length of a rectangle is 14 feet more than the width. If the perimeter of the rectangle is 72 feet, what are its dimensions?
In Exercises 77–78, use a coding matrix A of your choice. Use a graphing utility to find the multiplicative inverse of your coding matrix. Write a cryptogram for each message. Check your result by decoding the cryptogram. Use your graphing utility to perform all necessary matrix multiplications.
In Exercises 77–80, determine whether each statement makes sense or does not make sense, and explain your reasoning.I multiplied an m × n matrix and an n × p matrix by multiplying corresponding elements.
In Exercises 77–80, determine whether each statement makes sense or does not make sense, and explain your reasoning.I’m working with two matrices that can be added but not multiplied.
In Exercises 79–82, determine whether each statement makes sense or does not make sense, and explain your reasoning.I found the multiplicative inverse of a 2 × 3 matrix.
Find all zeros of f(x) = x3 - 4x2 + x + 6.
Exercises 80–82 will help you prepare for the material covered in the first section.Consider the equationa. Set y = 0 and find the x-intercepts.b. Set x = 0 and find the y-intercepts. zł 1² 9 4 = 1.
In Exercises 77–80, determine whether each statement makes sense or does not make sense, and explain your reasoning.I’m working with two matrices that can be multiplied but not added.
In Exercises 79–82, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used Gauss-Jordan elimination to find the multiplicative inverse of a 3 × 3 matrix.
Fill in each blank so that the resulting statement is true.Consider the following equation in standard form:The value of a2 is_______ , so the x-intercepts are______ and__________ . The graph passes through_________ and_________ , which are the vertices. The value of b2 is_________ , so the
In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).x2 = 4y ندی * -4-3-2 -4-3 8 X 8. 2- د D ه ن دا + I 4. b.
In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci. -4-3-1. 321 y 4 ----- X
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (0, 20); Directrix: y = -20
In Exercises 15–22, graph each hyperbola. Locate the foci and find the equations of the asymptotes.x2 - y2 - 2x - 2y - 1 = 0
In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci. II +4 -4-3-2-1 1 2 3 4 & 3 III 3- ||| x
In Exercises 19–22, find the standard form of the equation of the conic section satisfying the given conditions.Hyperbola; Foci: (-4, 5), (2, 5); Vertices: (-3, 5), (1, 5)
In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.4x2 - 25y2 = 100
A semielliptical archway over a one-way road has a height of 10 feet and a width of 30 feet. A truck has a width of 10 feet and a height of 9.5 feet. Will this truck clear the opening of the archway?
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (0, -25); Directrix: y = 25
In Exercises 23–24, find the standard form of the equation of each hyperbola satisfying the given conditions.Foci: (0, -4), (0, 4); Vertices: (0, -2), (0, 2)
In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci. -4-3-2- (-1,-1) 432 4. 1 2 3 4 T www.w x
In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.9y2 - 25x2 = 225
A lithotriper is used to disintegrate kidney stones. The patient is placed within an elliptical device with the kidney centered at one focus, while ultrasound waves from the other focus hit the walls and are reflected to the kidney stone, shattering the stone. Suppose that the length of the major
In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. y = ± √x² - 2
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (0, -15); Directrix: y = 15
In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.16y2 - 9x2 = 144
In Exercises 27–33, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.y2 = 8x
An explosion is recorded by two forest rangers, one at a primary station and the other at an outpost 6 kilometers away. The ranger at the primary station hears the explosion 6 seconds before the ranger at the outpost.a. Assuming sound travels at 0.35 kilometer per second, write an equation in
In Exercises 13–26, use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. y = ± √x²-3
Radio tower M2 is located 200 miles due west of radio tower M1. The situation is illustrated in the figure shown, where a coordinate system has been superimposed. Simultaneous radio signals are sent from each tower to a ship, with the signal from M2 received 500 microseconds before the signal from
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Vertex: (2, -3); Focus: (2, -5)
In Exercises 27–32, find the standard form of the equation of each hyperbola. y NI HIV WA 4- -2-11- 12 4 X
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Foci: (-5, 0), (5, 0); vertices: (-8, 0), (8, 0)
Explain why it is not possible for a hyperbola to have foci at (0, -2) and (0, 2) and vertices at (0, -3) and (0, 3).
In Exercises 27–32, find the standard form of the equation of each hyperbola. A II H-B y ..... K 2000 12 I x
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Vertex: (5, -2); Focus: (7, -2)
In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).(x + 1)2 = 4(y + 1) b. a. 1 + 2 + 3 2 X 2 HE y A d. y C. 3 2 TI Y X ### النا ل لنا ISD N
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Foci: (-2, 0), (2, 0); vertices: (-6, 0), (6, 0)
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (3, 2); Directrix: x = -1
In Exercises 27–32, find the standard form of the equation of each hyperbola. CITI I I+ -2-1 CII 3- 1 2 4 IIII X
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Foci: (0, -4), (0, 4); vertices: (0, -7), (0, 7)
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (2, 4); Directrix: x = -4
In Exercises 27–33, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.x2 + 16y = 0
In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).(y - 1)2 = 4(x - 1) b. a. 1 + 2 + 3 2 X 2 HE y A d. y C. 3 2 TI Y X ### النا ل لنا ISD N
In Exercises 27–32, find the standard form of the equation of each hyperbola. e -2-1 y HA 2 3/4/5 NIT WEN X
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Foci: (0, -3), (0, 3); vertices: (0, -4), (0, 4)
In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions.Focus: (-3, 4); Directrix: y = 2
In Exercises 27–33, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(y - 2)2 = -16x
In Exercises 27–32, find the standard form of the equation of each hyperbola. 3 CJ X ㅂ + HV
In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).(x + 1)2 = -4(y + 1) b. a. 1 + 2 + 3 2 X 2 HE y A d. y C. 3 2 TI Y X ### النا ل لنا ISD N
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Foci: (-2, 0), (2, 0); y-intercepts: -3 and 3
In Exercises 27–33, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.(x - 4)2 = 4(y + 1)
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Foci: (0, -2), (0, 2); x-intercepts: -2 and 2
In Exercises 27–33, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.x2 + 4y = 4
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Major axis horizontal with length 8; length of minor axis = 4; center: (0, 0)
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x + 2)² (v1)² 9 25 = 1
In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).(y - 1)2 = -4(x - 1) b. a. 1 + 2 + 3 2 X 2 HE y A d. y C. 3 2 TI Y X ### النا ل لنا ISD N
In Exercises 33–42, use the center, vertices, and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes. (x + 3)² 25 y² 16
In Exercises 27–33, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola.y2 - 4x - 10y + 21 = 0
In Exercises 37–50, graph each ellipse and give the location of its foci. (x - 1)² (y + 2)² + 16 9 = 1
In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions.Major axis horizontal with length 12; length of minor axis = 6; center: (0, 0)
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