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- A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the direction of maximum temperature increase. If the temperature at (x, y) is T(x, y) = -e-2y cos x, find an equation y = ƒ(x) for the path of a heat-seeking particle at the point (π/4, 0).find a general soltion to the third order equation y''' + y'' + 3y' -5y =0solve for the coodinates of ther point for (b) and (c) as well
- Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solutionfind the position function of the particle moving along a line that satisfies the given conditions. a(t)=4sin(t)-cos(t), s(0)=5, v(0)=0The position P(x, y) of a particle moving in the xy-plane is given by the equations and parameter interval x = √t, y = t, t ≥ 0. Identify the path traced by the particle and describe the motion.
- The total surface area S of a right cir-cular cylinder is related to the base radius r and height h by the equation S = 2pai r2 + 2pai rh. a. How is dS/dt related to dr/dt if h is constant? b. How is dS/dt related to dh/dt if r is constant? c. How is dS/dt related to dr/dt and dh/dt if neither r nor h is constant? d. How is dr/dt related to dh/dt if S is constant?find a general soltion to y" +2y' +4y =0Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in terms of x and y.) z = e6x2 + 8y2, P(0, 0, 1)