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- Suppose you are climbing a hill whose shape is given by the equation z = 1,300 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (80, 80, 1204). The positive x-axis points east and the positive y-axis points north.Find the relationship between x and y such that the point (x,y) is equidistance from the points (7,1) and (3,5)Find equations of the two lines that are tangent to the circle x2 + y2 = 1 and pass through the point (0, 3). (Hint: Let y - mx + 3, and determine conditions on m that will ensure that the system has only one solution.)
- show that a=(2x^2+8xy^2z)i+(3x^3y-3xy)j-(4y^2z^2+2x^3z)k is not a solenoidal but b=(xyz^2.A) is solenoidal7. The three planes x + y + z = 0, x + 2y + 2z = 1, and 2x − y + mz = n intersect in a line. Determine the values of m and n for which this is true.Enclosed by the cylinders z= x2 y = x 2 and the planes z =0 y =4
- 1. Solve by Cramer’s rule 3x + y + 4z = 11 4x – 4y + 6z = 11 6x – 6y = 3 2. Find the volume of tetrahedron given the following (1, 0, 1), (0, 1, 0), (0, 0, 1), and (1, 1, 1).7- Given the parallelogram, solve for x 8- Given the parallelogram where RD=x+13RD=x+13 and DT=3x-3DT=3x−3, solve for x.Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed by the part of y = 1 − x^2 from x = −2 ax = 2, followed by the segment from (2, −3) to (4, b).