Brett Moore Assignment Section 11.5 due 09/10/2015 at 10:00pm MST 4. (1 pt) 1. (1 pt) x y Suppose w = + , where y z x = e3t , y = 2 + sin (2t), and z = 2 + cos (5t). A ) Use the chain rule to nd dw as a function of x, y, z, and dt t. Do not rewrite x, y, and z in terms of t, and do not rewrite e3t as x. dw dt Choi MAT 267 ONLINE A Fall 2015 Let w = 3xy 4yz + 2xz, x = st, y = est , z = t 2 Compute w (3, 2) = s w (3, 2) = t 5. (1 pt) = Note: You may want to use exp() for the exponential function. Your answer should be an expression in x, y, z, and t; e.g. \"3x - 4y\" B ) Use part A to evaluate dw when t = 0. dt Let W (s,t) = F(u(s,t), v(s,t)) where u(1, 0) = 6, us (1, 0) = 1, ut (1, 0) = 9 v(1, 0) = 5, vs (1, 0) = 5, vt (1, 0) = 4 Fu (6, 5) = 8, Fv (6, 5) = 4 2. (1 pt) Suppose z = x2 sin y, x = s2 5t 2 , y = 6st. z A. Use the chain rule to nd s and z as functions of x, y, s t and t. z s Ws (1, 0) = 6. (1 pt) Consider the curve x2 + 5xy + y3 = 7 The equation of the tangent line to the curve at the point (1, 1) has the form y = mx + b where m= and b = 7. (1 pt) Consider the surface F(x, y, z) = x3 z4 + sin(y2 z4 ) + 1 = 0. Find the following partial derivatives = z t = B. Find the numerical values of (2, 2). z s and when (s,t) = z x z y = = (2, 2) = 3. (1 pt) Use the chain rule to nd z s and z t , First the pieces: z x = z y x t y t 8. (1 pt) The radius of a right circular cone is increasing at a rate of 3 inches per second and its height is decreasing at a rate of 4 inches per second. At what rate is the volume of the cone changing when the radius is 10 inches and the height is 40 inches? NOTE: The volume of a cone with base radius r and height h is given by V = 1 r2 h. 3 cubic inches per second where z = exy tan y, x = 1s + 1t, y = x s y s z t (2, 2) = z t z s Wt (1, 0) = 2s 7t 9. (1 pt) In a simple electric circuit, Ohm's law states that V = IR, where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.04 volts per second and, as the resistor heats up, the resistance is increasing at 0.01 ohms per second. When the resistance is 400 ohms and the current is 0.02 amperes, at what rate is the current changing? amperes per second = = = = = And putting it all together: z z x z y z z x z y s = x s + y s and t = x t + y t 1 Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America 2