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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Use the quotient rule to simplify the expression. Use positive exponents to write your answer. 21x-3y4 7xy
Use the rule of 70 to estimate the annual percent rate of growth for a city whose population P doubles in time T. P = 150,000, T = 40 years
Factor the expression completely. 2x²14x + 20
Write the expression in radical notation.(x-y)-2/7
Factor the expression completely. 7x² + 35x + 42
Simplify. Leave numerators and denominators in factored form when appropriate. x² + x - 12 2x²-9x-5 x² + 7x + 12 2x² - 7x-4
Find the volume, the surface area of the side, and the total surface area of the cylinder that satisfies the given conditions, where r is the radius and h is the height. Approximate values to the nearest tenth. r is one-fourth of h, and h = 2.1 feet
Write the expression in radical notation. Then evaluate the expression when the result is an integer.272/3
Write the expression in radical notation. Then evaluate the expression when the result is an integer.84/3
Use the quotient rule to simplify the expression. Use positive exponents to write your answer. 32x³y -24x³y
Use the rule of 70 to estimate the annual percent rate of growth for a city whose population P doubles in time T. P = 400,000, T = 25 years
Simplify. Leave numerators and denominators in factored form when appropriate. x-2 x³ - x +² - 2x x²-1
Write the expression in radical notation. Then evaluate the expression when the result is an integer.(-1)4/3
Simplify. Leave numerators and denominators in factored form when appropriate. x² - 2x - 35 2x³ - 3x² x²-r 2x 14 -
Find the volume and surface area of the sphere satisfying the given condition, where r is the radius and d is the diameter. Approximate values to the nearest tenth. r = 3 feet
Use the graph to find the standard form of the hyperbola. 6
Approximate the constant of variation to the nearest hundredth.The variable z varies jointly with the second power of x and the third power of y. If x = 2 and y = 2.5, then z = 31.9.
Approximate the constant of variation to the nearest hundredth.The variable z varies jointly with the 1.5 power of x and the 2.1 power of y. If x= 4 and y = 3.5, then z = 397.
The variable z varies jointly with the square root of x and the cube root of y. If z = 10.8 when x = 4 and y = 8, find z when x = 16 and y = 27.
The variable z varies jointly with the third powers of x and y. If z = 2160 when x = 3 and y = 4, find z when x = 2 and y = 5.The variable z varies jointly with the second power of x and the third power of y. Find the constant of proportionality if z = 2160 when x = 3 and y-4 and then find z when x
A hyperbola with an equation of the formhas a(n) vertical/horizontal transverse axis. 11 1
An ellipse with equationhas a(n) vertical/horizontal major axis. + 12 = 1(a>b> 0)
Write in intercept form the equation of the line satisfying the given conditions. Then find the x- and y-intercepts of the line.Passing through (-2, 6) and (4, -3)
Graph the parabola defined by x = 1/2y2. Include the focus and directrix.
Graph the ellipse. Label the foci and the endpoints of each axis. 1= 9 für 월을
The_______ are the endpoints of the transverse axis of a hyperbola.
The endpoints of the major axis of an ellipse are called the _______ of the ellipse.
Write in intercept form the equation of the line satisfying the given conditions. Then find the x- and y-intercepts of the line.Passing through (-6, -4) and (3, 8)
Find an equation of the parabola with focus (-1,0) and directrix y = 3.
A parabola always opens toward its__________.
Graph the hyperbola defined by x2/9 - y2/16-= 1. Include the foci and asymptotes.
The (dashed) rectangle used as an aid in graphing a hyperbola is called the_______ rectangle.
The foci of an ellipse are located on the__________ axis.
Write in intercept form the equation of the line satisfying the given conditions. Then find the x- and y-intercepts of the line.Slope -2, passing through (3,-1)
Graph the ellipse defined by x2/36+y2/100= 1. Include the foci and label the major and minor axes.
A parabola always opens away from its_________.
The parabola x2 = 4py opens________ if p > 0. and it opens________ if p < 0.
Sketch a graph of a hyperbola, centered at the origin, with the foci, vertices, and asymptotes shown in the figure. Find an equation of the hyperbola. (The coordinates of the foci and vertices are integers.) -8 F2 00 x
Determine an equation of the conic section that satisfies the given conditions.Hyperbola with vertices (-2 ± 3, 3) and foci given by (-2 ± 4, 3)
Use mathematical induction to prove the statement. Assume that n is a positive integer. 1² +2²+ 3² + + n² n(n + 1)(2n + 1) 6
Use the graphical representation to identify the terms of the finite sequence. 6 5 M 0 1 2 3 4 5 6
Sketch a graph of a hyperbola, centered at the origin, with the foci, vertices, and asymptotes shown in the figure. Find an equation of the hyperbola. (The coordinates of the foci and vertices are integers.) F₂ V 2. ●●+ V₁ F₁8 X
Find the standard equation of the ellipse shown in the figure. Identify the coordinates of the vertices, endpoints of the minor axis, and the foci. 딤 2 2
Match the equation with its graph (a-f). x² = 2y
Find an equation of the parabola with vertex (0, 0) that satisfies the given conditions. Focus (0,2)
Write the equation in standard form for an ellipse or a hyperbola centered at (h, k). Identify the center and the vertices. 4y² + 8y3x² + 6x = 11
Sketch a graph of the ellipse. (x - 2)² 4 - (v − 1)² 9 1
Match the equation with its graph (a-d). ,
Write the equation in standard form for an ellipse or a hyperbola centered at (h, k). Identify the center and the vertices. x² + 4x - 4y² + 24y = 36
Find an equation of the parabola with vertex (0, 0) that satisfies the given conditions.Directrix y = 2
Write the equation in standard form for an ellipse or a hyperbola centered at (h, k). Identify the center and the vertices. 5x² + 20x + 2y²-8y = -18
Sketch a graph of the hyperbola. Identify the vertices, foci, and asymptotes. (y + 1)² = (x - 3)² 4 =
Translate the ellipse with the given equation so that it is centered at the given point. Find the new equation and sketch its graph. 15 16 = 1; (5, -6)
Match the equation with its graph (a-d). ,
Sketch a graph of the ellipse. (x + 1)² (v + 3)² 16 9 + 1
Match the equation with its graph (a-d). ,
Find an equation of the parabola with vertex (0, 0) that satisfies the given conditions.Directrix x = 2
Sketch a graph of the ellipse. (x + 1)² (y + 2)² + 16 25 1
A searchlight is constructed in the shape of a paraboloid with a depth of 7 inches and a diameter of 20 inches, as illustrated in the figure. Determine the distance d that the bulb should be from the vertex in order to have the beam of light shine straight ahead. 7 in.- 20 in.
Give graphical and numerical representations of the sequence defined by an = -2n + 3, where an = f(n). Include the first six terms.
Write 34,500 in scientific notation and 1.52 x 10-4 in standard form.
Complete the following. (a) Write the described sequence. (b) Write a series that sums the terms of the sequence in part (a). (c) Find the sum of the series in part (b).The counting numbers from 1 to 5
Does the number represent a probability? 2.5
Calculate the number of distinguishable strings that can be formed with the given number of a's and b's. Four a's, two b's
Solve -2.3x + 3.4 = √2x2 - 1 graphically. Round your answers to the nearest tenth.
Of a group of 82 students, 19 are enrolled in music, 22 in art, and 10 in both. (a) Draw a Venn diagram representing these data. (b) Use this diagram to determine the probability that a student selected at random is enrolled in music, art, or both. (c) Solve part (b) symbolically by
Find a general term an for the arithmetic sequence. a4 = 2, a7 = -7
Use Pascal's triangle to help expand the expression. (3-2x)5
A hyperbola with an equation of the formhas a(n) vertical/horizontal transverse axis. || 1
An ellipse with equationhas a(n) vertical/horizontal major axis. 3 + 2 = = 1 (a> b > 0)
Write in intercept form the equation of the line satisfying the given conditions. Then find the x- and y-intercepts of the line.Slope 4, passing through (-2, 1)
Find an equation of the ellipse centered at (3,-2) with a vertical major axis of length 6 and minor axis of length 4. What are the coordinates of the foci?
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the foci and vertices. 9 로 49
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the foci and vertices. 등이 4
Find the x- and y-intercepts of the ellipse. ² +²²=₁ 1 25 9
Graph the ellipse. Label the foci and the endpoints of each axis. 1
Match the equation with its graph (a-f). x² = 2y
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the foci and vertices. P²__x² 36 16
Write 9y2 - 54y - 16x2 - 32x = 79 in the standard form for a hyperbola centered at (h, k). Identify the center and the vertices.
Graph the ellipse. Label the foci and the endpoints of each axis. 36 16
A parabolic reflector for a searchlight has a diameter of 4 feet and a depth of 1 foot. How far from the vertex should the filament of the light bulb be located?
The parabola y2 = 4px opens________ if p > 0. and it opens________ if p < 0.
Find the x- and y-intercepts of the ellipse.Vertices (0, ±13) and foci (0, ±12)
The parabola x2 = 4py has a vertical/horizontal axis of symmetry.
Sketch a graph of the parabola. x² = y
The parabola y2 = 4px has a vertical/horizontal axis of symmetry.
Write x2 - 4x + 4y2 + 8y = 8 = 0 in the standard form for an ellipse centered at (h, k). Identify the center and the vertices.
Graph the ellipse. Label the foci and the endpoints of each axis. + 라
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the foci and vertices. 4 X 4 || 1
Match the equation with its graph (a-f). y² = -3x
Sketch a graph of the parabola. x² = -y
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the foci and vertices. x² - y² = 9
Match the equation with its graph (a-f). b = ₂² + 2x
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the foci and vertices. 49²25x²= 1225
Graph the ellipse. Label the foci and the endpoints of each axis. x² + 4y² = 400
Sketch a graph of the parabola. =-X
Sketch a graph of the hyperbola, including the asymptotes. Give the coordinates of the foci and vertices. 9y² - 16x² = 144
Match the equation with its graph (a-f). 36 49 1
Graph the ellipse. Label the foci and the endpoints of each axis. 9x² + 5y² = 45
Graph the ellipse. Label the foci and the endpoints of each axis. 25x² +9y² = 225
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