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An engineer is building experimental, dome-shaped living quarters 304 m high and modeled by the function z = 304 - 4x² - 8y²2. She wants to bolt a flat solar panel to the dome at the point (5, 5,4). Find the vector of the direction in which the engineer should drill. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) direction:
Consider the surface 10x² - 5y² - 72²2 = -103. (a) Find the equation of the tangent plane to the surface at the point (2, 4, 3). (Use symbolic notation and fractions where needed.) tangent plane: 40x + 40y-42z = 366 Incorrect
Determine the point(s) on the surface z = 24x - 12y - 4x² − 3y² at which the tangent plane is parallel to the xy-plane. (Give your answer as a comma-separated list of coordinate points of the form (*, *, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) (x, y, z) = Incorrect (3,-2,k)
Consider the surface z = 2x² - 6y². (a) Find the equation of the tangent plane to the surface at the point (5, 4, -12). (Use symbolic notation and fractions where needed.) tangent plane: (b) Find the symmetric equations of the normal line to the surface at the point (5,4,-12). Select the correct symmetric equations of the normal line. x - 20 y + 48 5 4 x-5 20 x + 5 20 x-5 20 = 11 = = 48 y +4 48 y-4 48 || = = z+1 12 z + 12 1 z - 12 1 z + 12 1
Find an equation of the tangent plane to the surface z = √√√x² + 35y² at the point (1, 1,6). (Express numbers in exact form. Use symbolic notation and fractions where needed. Let z = f(x, y) and give the equation in terms of x, y, and z.) tangent plane: x+y+√√2z−2−6√√/2=0 Incorrect