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An curve has equation y =12/3 -2x
Find dy/dx
Let S be the surface of the solid D that is bounded below by the paraboloid z = x 2 + y 2 + 1 and bounded above by the plane z = 5. Use Gauss’ Theorem to determine the flux integral Z S F · n dS, where F (x, y, z) = (xz, 1 − yz, xz).
Consider the surface S = (x, y, z) ∈ R 3 | z = 3 − x 2 − y 2 ; z ≥ 2 . Assume that S is oriented upward and let C be the oriented boundary of S. (a) Sketch the surface S in R 3 . Also show the oriented curve C and the XY-projection of the surface S on your sketch. (2) (b) Let F (x, y, z) = (2y, 3z, 4y). Evaluate the flux integral Z Z S (curl F) · n dS by i. determining curl F and the upward unit normal n of S and using the formula (17.2) on p. 104 of Guide 3 (5) ii. Using Stokes’ Theorem, convert the given flux integral to a line integral.
Consider the surface S = n (x, y, z) | z = p x 2 + y 2 and 1 ≤ z ≤ 3 o .(a) Sketch the surface S in R 3 . Also show its XY-projection on your sketch. (2) (b) Evaluate the area of S, using a surface integral
Consider the force field F defined by F (x, y) = (6xy-12,3x^2). Use the formula (16.2) on p.90 of Guide 3 to determine the work done by the force field F in moving an object in an anticlockwise direction from the point (2, 0) to the point (−2, 0) along the circle x 2 + y 2 = 4 by applying (a) the method for evaluating a line integral that is described in Example 16.4.1 (4) (b) the Fundamental Theorem of Line Integrals (Theorem 16.5.2).
(Section 13.3 and Chapter 14) Let D be the region in R 3 p that lies inside the cone z = x 2 + y 2 above the plane z = 1 and below the hemisphere z = p 4 − x 2 − y 2 . (a) Sketch the region D in R 3 .(b) Express the volume of D as a sum of triple integrals, using cylindrical coordinates.
Determine the slope-intercept form of a linear equation, given the listed attributes: a) Slope = -2 and y-intercept = (0,10) b) Slope = -3 and (4, -2) lies on line c) Slope = 0 and (2,4) lies on line d) (3, -2) and (-12,1) lies on line e) (20, 240) and (15,450) lies on line
A. Find the slope, x-intercept and y-intercept form of the following equations a) 5x + 2y =-10 b) 13y -2x = 3 c) 25𝑦 + 31𝑥 − 18 = 10𝑦 d) −3𝑥 + 4𝑦 − 10 = 7𝑥 − 2𝑦 + 50
#340153 on Dec 2023