Find the constants m and n such that the surface mx2 − 2nyz = (m + 4)x will be orthogonal to the surface 4x 2 y + z 3 = 4 at the point (1, −1, 2).
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Find the directional derivative of x 2 y 2 z 2 at the point (1, 1, −1) in the direction of the tangent to the curve x = e t , y = sin 2t + 1, z = 1 − cost at t = 0.
Q 4.68a) Find the values of the constants a, b, and c so that the directional derivative of Ф , 2. -1) has a maximum of magnitude 64 in a direction parallel to the z axis. ay + by2+cz, Find the acute angle berween the surfaces y'3x+ and 3x2-y + 2z I at the point (1, -2, 1). Find the constants a and b so that the surface ax -by-(a+2)x will be orthogonal to the surface y+ 4 at the...
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
Consider the following. z = x2 + y2, z = 36 − y, (6, -1, 37) (a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. x − 6 12 = y + 1 −2 = z − 37 −1 x − 6 1 = y + 1 12 = z − 37 −12 x − 6 = y + 1 = z − 37 x − 6 12 =...
Question 3. Consider the function h: R3 → R h(x, y, 2) = (x2 + y2 + 2) +3/(x2 + 2xy + y) (a) What is the maximal domain of h? Describe it in words. (it may help to factor the denominator in the second term) > 0 for any a, (b) It is difficult to immediately find the range of h. Using the fact that a show that h cannot take negative values. Can h be an onto function?...
(1 point) Are the following statements true or false? ? 1. If z is orthogonal to uị and u2 span(uj, u2), then z must be in and if W = Wt. ? 2. For each y and each subspace W, the vector y – projw(y) is orthogonal to W. ? 3. If y is in a subspace W, then the orthogonal projection of y onto W is y itself. ? 4. The orthogonal projection p of y onto a subspace...
([8]) Find the point on the surface z = x2 + 2y2 where the tangent plane is orthogonal to the line connecting the points (3,0,1) and (1,4,0). Useful formula: The curvature of the plane curve y = f(x) is given by k(x) = \f"|(1 + f/2)-3/2, ([9]) Use spherical coordinates to find the volume of the solid situated below x2 + y2 + 2 = 1 and above z= V x2 + y2 and lying in the first octant.
PLEASE DO LETTER d.) PLEASE DO LETTER f.) The plane from e.) is 4(x-2)+6(y-1)+(z-1)=0 or 4x+6y+z=15 15. The temperature on an unevenly heated metal plate positioned in the first quadrant of the xy-plane is given by 25xy + 25 C(x, y) = 7 (x - 1)2 + (y - 1)2 +1° Assume that temperature is measured in degrees Celsius and that x and y are each measured in inches. (Note: At no point in the following questions should you expand...
show all work and explanations for problem 4. please. thanks #3, 4: (a) determine whether lies in , f is par- allel to o but not in ø, or l and go are concurrent. (b) If l and o are concurrent, find the intersection point and the angle between them. (c) Find the plane that includes f and is orthogonal to g. simply y+4 3, -1 ZI2 3. l: x = : 2x + 3y -z+14 = 0 3 (x...
Hi, I need help solving number 13. Please show all the steps, thank you. :) Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...