Find the centroid of the region that is bounded below by the x-axis and above by...
three a) Sketch the graph and complete the table for the polar equation 5-2cose Type of conic section (x, y) coordinates of vertex or vertices Eccentricity (x,y) coordinates of the focus or the foci (x,y) coordinates of the x intercept (x,y) coordinates of the y intercept Domain in interval notation Range in interval notation (x,y) equation of the directrix or directrices (x,y) coordinates of the center Standard equation in (x,y) variables three a) Sketch the graph and complete the table...
Graph the following conic section, identify the vertices, foci, directrices, and asymptotes (if they exist). Use a graphing utility to check your work OA. OB r= 10 - 10 sin 0.6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Express your answer using Cartesian coordinates. O A. The focus/i is/are (Type an ordered pair. Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. There...
Find the focus and directrix of the parabola with the equation 8x2 + 8y = 0. Then choose the correct graph of the parabola. What are the coordinates for the focus of the parabola? (Type an ordered pair.) What is the equation for the directrix? Choose the correct graph for 8x² + 8y = 0 below. O N4
Find an equation of the ellipse that has center (0, -3), a minor axis of length 10, and a vertex at (-9, -3).Below is the graph of a parabola with its vertex and another point on the parabola labeled. Write an equation of the parabola.
Use polar coordinates to find the centroid of the following constant-density plane region The region bounded by the cardioid r4+4cos0. Set up the double integral that gives the mass of the region using polar coordinates. Use increasing limits of integration. Assume a density of 1 dr d0 (Type exact answers.) Set up the double integral that gives My the plate's first moment about the y-axis using polar coordinates. Use increasing limits of integration. Assume a density of M,-J J O...
Let R be the region shown above bounded by the curve C = C1[C2. C1 is a semicircle with center at the origin O and radius 9 5 . C2 is part of an ellipse with center at (4; 0), horizontal semi-axis a = 5 and vertical semi-axis b = 3. Thanks a lot for your help:) 1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
The region R is bounded by the x-axis and y = V16 – x2 a) Sketch the bounded region R. Label your graph. b) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) da c) R
The equation of a hyperbola is 4x -(y+3) 9 a) Find the center, vertices, transverse axis, and asymptotes of the hyperbola b) Use the vertices and the asymptotes to graph the hyperbola a) The center of the hyperbola isType an ordered pair.) The vertices are Type an ordered pair. Use a comma to separate answers as needed.) The equation of the transverse axis is (Type an equation.) Determine the equations of the asymptotes. Choose the correct answer below b) Choose...
Consider the equation below. 9 7 - 8 sin(e) (a) Find the eccentricity. e = x (b) Identify the conic. O ellipse O parabola hyperbola O none of the above (c) Give an equation of the directrix (in Cartesian coordinates). (d) Sketch the conic. 10 -15 10
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Ry region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R