1. Let be the solid b lev lw the cos (n) Find the volume of E. y and the plane 33 10 (b) Find an equation of the plane tangent to the cone z = (1. 1. 2). Write the swer in the form of a by d Are real numbers 1y at the point , wluereb , w l triple integral that et t e blue f + 2 Set literateleira D eber .) of Write it Let the...
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T, and let T be the plane defined by x–5y+z = 22. Find the point Q where L and T intersect. Q=(0,0,0)
Let D be a region in the (x, y)-plane. If a, b,c >0, let Sa be the part of the hyperbolic paraboloid z = axy in R3 with (x,y) E D, and let Tổ.c be the part of the elliptic paraboloid·bz2 + суг in R3 with (x,y) D. For a given a > 0, find b,c >0 such that Tb,e has the same area as Sa Let D be a region in the (x, y)-plane. If a, b,c >0, let...
please show steps 201701559 Question 10 Let a,b,c be the last digits of your student ID Find the equation of the plane that passes through the point (a,b,c) and that is parallel to the plane containing the the parallel lines x = (a + b + c).y=(a+b+c)2(a+b+c+1)) and x = a +(a+b+c)t.y=b+la+b+c),2--5+(a + b +C+1)
Need it asap show work please Let i + 2z B(2) = 4- 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, B(2) < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from -i to e3ri/4 and then bouncing from e3mi/4 to 1. Denote by the curve representing the trajectory of the particle. Without evaluating the...
10. Stokes' Theorem and Surfac e Integrals of Vector Fields a. Stokes' Theorem: F-dr= b. Let S be th ky-plane. Draw a sketch of curve C in the xy-plane. et be the surface of the paraboloid z 4-x-y and Cis the trace of S in the c Let Fox.y.z) <2z, x, y>, Compute the curl (F) d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) F-dr Use Stokes' Theorem to compute , e. 10. Stokes' Theorem and Surfac...
Part 15A and 15B (15) Let n E Z+,and let d be a positive divisor of n. Theorem 23.7 tells us that Zn contains exactly one subgroup of order d, but not how many elements Z has of order d. We will determine that number in this exercise. (a) Determine the number of elements in Z12 of each order d. Fill in the table below to compare your answers to the number of integers between 1 and d that are...
8. Let E be the solid in the first octant bounded by: the plane 2x + y + z = 8, the vertical cylinder y = x2, and the coordinate planes x = 0 and z = 0. For each of the three parts below you must illustrate your solution with diagrams in 2 and 3 dimensions. Marks will be given for the quality of the diagrams and how they are able to help the reader understand the way in...
4. Let D be a region in the (ar,y)-plane. If a, b,c > 0, let S be the part of the hyperbolic paraboloid ary in R3 with (r, y) E D, and let Thc be the part of the elliptic paraboloid :-bz2 + суг in R3 with (z, y) E D. For a given a >0, find b,>0 such that The has the same area as S
6. Let B(2) = i + 2z 4 - 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, |B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ri/4 and then bouncing from e3vi/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how...