Decide whether the given sequence is finite or infinite.-4,
Decide whether the given sequence is finite or infinite.-4, -3, -2, -1 Finite Infinite 2.1 points Question 2 Evaluate the expression.(10 2) 1,814,400 22 5 45 2.1 points Question 3 Evaluate the series, if it converges.9 – + – + . . . – 1 8 Does not converge 2.1 points Question 4 Evaluate the sum. 218 173 124 162 2.1 points Question 5 Evaluate the sum. Round to the nearest hundredth, if necessary. 42 20 44 54 2.1 points Question 6 Evaluate the terms of the sum using the given information.x 1 = 4, x 2 = 1, x 3 = 0, and x 4 = -1 12 – 3 + 4 + 5 -20 – 5 – 4 – 5 -12 + 5 – 4 + 5 -20 + 3 – 4 – 3 2.1 points Question 7 Find a general term an for the geometric sequence.a 1 = 3, r = 3 an = 6n an = 3n an= 3 + 6(n – 1) an = 3n-1 + 2 2.1 points Question 8 Find a rectangular equation for the plane curve defined by the parametric equations.x = , y = 2t + 5, for t in (0, ∞) y = 2 + 5, x in (0, ∞) y = 2×2 + 5, x in (0, ∞) y = 2 – 5, x in (0, ∞) y = 2×2 – 5, x in (0, ∞) 2.1 points Question 9 Find an equation for the conic. If the conic is a parabola, assume that the vertex is at the origin. If the conic is an ellipse or hyperbola, assume that it is centered at the origin.Focus at (0, -6) and e = 1 y = – x2 x = – y2 y = x2 y = – x2 2.1 points Question 10 Find an equation for the parabola with vertex at the origin.Through (9, 8), opening to the right y = x2 x = – y2 x = y2 x = y2 2.1 points Question 11 Find an equation of a parabola that satisfies the given conditions.Vertex (3, -10), focus (3, -8) 8(y – 10) = (x + 3)2 (y + 10)2 = 8(x – 3) (x – 3)2 = 8(y + 10) y – 10 = 8(x + 3)2 2.1 points Question 12 Find an equation of the ellipse.An ellipse with center at origin, length of major axis 6 and y-intercepts + = 1 + = 1 + = 1 + = 1 2.1 points Question 13 Find an equation of the hyperbola.Vertices at (0, 3), (0, -3); foci at (0, 9), (0, -9) – = 1 – = 1 – = 1 – = 1 2.1 points Question 14 Find the center and radius of the circle.x 2 + y 2 + 12x – 2y = -1 (1, -6), r = 6 (6, -1), r = 36 (-1, 6), r = 36 (-6, 1), r = 6 2.1 points Question 15 Find the center-radius form for the circle having the given endpoints of a diameter.( -3, -5) and (7, 7) (x + 2)2 + (y + 1)2 = -11 (x + 2)2 + (y + 1)2 = 61 (x – 2)2 + (y – 1)2 = -11 (x – 2)2 + (y – 1)2 = 61 2.1 points Question 16 Find the center-radius form of the equation of the circle satisfying the given conditions.Center ( -10, 0), radius 1 (x + 10)2 + y2 = 1 x2 + (y – 10)2 = 1 (x – 10)2 + y2 = 1 x2 + (y + 10)2 = 1 2.1 points Question 17 Find the common difference for the arithmetic sequence.3, 5, 7, 9, … 2 0.02 -2 6 2.1 points Question 18 Find the common ratio r for the given infinite geometric sequence.4, -12, 36, -108, 324, … -3 3 -16 – 2.1 points Question 19 Find the coordinates of the vertex and the direction of opening of each parabola.y = (x + 2) 2 + 7 (-7, 2) opens upward (7, -4) opens downward (7, -2) opens downward (-2, 7) opens upward 2.1 points Question 20 Find the eccentricity of the ellipse or hyperbola.x 2 – y 2 = 49 1 0 2.1 points Question 21 Find the first six terms of the sequence.a 1 = -9, a n = 5 ∙ a n-1 -9, -45, -225, -1125, -5625, -28,125 -9, -45, -40, -35, -30, -25 -45, -225, -1125, -5625, -28,125, -140,625 0, 5, -45, -40, -35, -30 2.1 points Question 22 Find the sum of the arithmetic series using a formula.1 + 3 + 5 + … + 515 66,049 66,822 66,564 67,081 2.1 points Question 23 Find the sum of the first n terms of the following arithmetic sequence.a 1 = -10, d = -2; n = 4. -40 -10 -52 -18 2.1 points Question 24 Find the sum of the geometric series. -156 -7710 -2460 244 2.1 points Question 25 Find anand a6 for the following arithmetic sequence.-1, 1, 3, 5, 7 an = 3n – 2; a6 = 16 an = n + 2; a6 = 8 an = 2n – 3; a6 = 9 an = -1(2)n-1; a6 = -32 2.1 points Question 26 For the given parabola, give the coordinates of the vertex, the axis, the domain, and the range.x = (y – 8) 2 + 6 vertex: (-6, 8);axis: y = 8;domain: [-6, ∞)range: (-∞, ∞); vertex: (8, 6);axis: y = 6;domain: [8, ∞)range: (-∞, ∞); vertex: (-6, -8);axis: y = -8;domain: [-6, ∞)range: (-∞, ∞); vertex: (6, 8);axis: y = 8;domain: [6, ∞)range: (-∞, ∞); 2.1 points Question 27 Give the focus, directrix, and axis for the parabola.- x 2 = y (0, -3), y = 3, y-axis (0, 3), y = -3, y-axis (-6, 0), x = 3, x-axis (0, -3), y = 3, x-axis 2.1 points Question 28 Graph the circle if possible.(x – 1) 2 + (y – 3) 2 = 16 2.1 points Question 29 Graph the ellipse. + = 1 2.1 points Question 30 Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges.a n = Converges Diverges 2.1 points Question 31 Graph the hyperbola. – = 1 2.1 points Question 32 Identify the equation as a parabola, circle, ellipse, or hyperbola.9x 2 + 4y 2 = 36 Circle Hyperbola Parabola Ellipse 2.1 points Question 33 Identify the type of graph. = 1 + The graph is a hyperbola that opens to the right and left. The graph is an ellipse with foci on the x-axis. The graph is an ellipse with foci on the y-axis. The graph is a hyperbola that opens upward and downward. 2.1 points Question 34 Solve the problem. A radio telescope has a parabolic surface. If it is 1 m deep and 16 m wide, how far is the focus from the vertex? 4 m 16 m 1 m 64 m 2.1 points Question 35 Solve the problem.A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 72 ft and the vertical clearance must be 24 ft at a point 12 ft from the center. Find an equation for the ellipse. + = 1 + = 1 + = 1 + = 1 2.1 points Question 36 Solve the problem.Find the sum of all the integers from -33 to 43. 418 342 385 375 2.1 points Question 37 Solve the problem.The annual population density of a species of insect after n years is modeled by a sequence. Suppose that the initial density of insects is 670 with r = 0.9. Write a recursive sequence that describes this data, where a n denotes the insect density during year n. Find the terms a 1 , a 2 , a 3 , …., a 5 . Round to two decimal places, if necessary. a1 = 603.00, a2 = 542.70, a3 = 488.43, a4 = 439.59, a5 = 395.63 a1 = 670, a2 = 670, a3 = 670, a4 = 670, a5 = 670 a1 = 670, a2 = 1273.00, a3 = 2418.70, a4 = 4595.53, a5 = 8731.51 a1 = 670 , a2 = 603.00, a3 = 542.70, a4 = 488.43, a5 = 439.59 2.1 points Question 38 Solve.The motion of a projectile that is fired at a 45° angle with the horizontal is given by x = v 0 t, for t in Suppose a projectile is fired with an initial velocity of 450 feet per second at an angle of 45° with the horizontal. Find (a) the time when it reaches maximum altitude (b) the maximum altitude. (a) 19.9 seconds(b) 6328 feet (a) 9.9 seconds(b) 1582 feet (a) 39.8 seconds(b) 3164 feet (a) 19.9 seconds(b) 1582 feet 2.1 points Question 39 Solve.The roof of a building is in the shape of the hyperbola where x and y are in meters. Determine the distance, w, between the outside walls. A = 7 m 22 m 8.7 m 4.7 m 9.4 m 2.1 points Question 40 Use the formula for Sn to find the sum of the first five terms of the geometric sequence. Round to the nearest hundredth, if necessary.3, -9, 27, -81, . . . 183 -363 363 -183 2.1 points Question 41 Use the summation properties and rules to evaluate the series. The following rules may be needed: . – 42 – 21 – 66 2.1 points Question 42 Which equation matches the given calculator-generated graph and description? Decide without using your calculator. Parabola; opens right 3y = x2 -3y = x2 -3x = y2 3x = y2 2.1 points Question 43 Write an equation for the parabola with vertex at the origin.Focus x2 = – y y2 = x x2 = -68y y2 = – x 2.1 points Question 44 Write out the first five terms of the sequence.a n = n 2 – n 0, 2, 6, 12, 20 1, 4, 9, 16, 25 2, 6, 12, 20, 30 0, 3, 8, 15, 24 2.1 points Question 45 Write the equation in standard form for an ellipse or a hyperbola centered at (h, k).9x 2 + 6y 2 + 36x – 18 = 0 + = 1 + = 1 + = 1 + = 1 2.1 points Question 46 Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).The first term is -1 + , and the common difference is 4; n = 3 -1 + , 4 + , 8 + 1 + , 3 + , 7 + -1 – , 3 + , 7 + -1 + , 3 + , 7 + 2.1 points Question 47 Write the indicated term of the binomial expansion.(3x + 2) 3; 3rd term 36x 72x 24 54×2 2.1 points Question 48 Write the sum of the geometric series as a rational number.0.45 + 0.0045 + 0.000045 + …
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