Calculus 3 :

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Section 11.3: Problem 6 {1 point] The gas law for a xed mass m. of an ideal gas at absolute temperature T, pressure P, and volume V is W = mRT, where R is the gas constant. Find the partial derivatives 8P MI W m2 HIV 5? 3T_L W_mR 8P 3V 3T _ W 55 (an Integer} Section 11.3: Problem 7 (1 point) Find the partial derivatives of the function f(x, y) = Tye ly You should as a by product verify that the function f satisfies Clairaut's theorem. f=(I, y) ve -9y v fy(I, y) xe 7+ gve -9y fry(I, y) le 97 _ ge -97 fur (I, y) 97 + 90Section 11.4: Problem 7 (1 point) Results for this submission Entered Answer Preview Result 2*pitrth 27Th correct (pi*r)^2 incorrect 0.1 0.1 correct 0.2 0.2 correct 542.87 542.87 correct At least one of the answers above is NOT correct. Use differentials to estimate the amount of material in a closed cylindrical can that is 60 cm high and 24 cm in diameter if the metal in the top and bottom is 0.1 cm thick, and the metal in the sides is 0.1 cm thick. Note, you are approximationg the volume of metal which makes up the can (ie. melt the can into a blob and measure its volume), not the volume it encloses. The differential for the volume is dV = 2xph dr+ (my)2 dh (enter your answer in therms of r and h ) ar 0.1 and dh = 0.2 (be careful) The approximate volume of material is 542.87 cmSection 11.5: Problem 1 (1 point) Suppose w = - + -, where y c=e", y = 2 + sin(5t), and = = 2 + cos(7t). 1. Use the chain rule to find dw dt as a function of , y, 2, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite elf as I. dw dt 109 Note: Your answer should be an expression in c, y, z, and t; e.g. "3x - 4y + 2t" dw 2. Use part 1. to evaluate when t = 0. dt 1215\\ 2 2Section 11.5: Problem 2 (1 point) Suppose = = x' sin(y) , I = 4s' -t', y = -6st. A. Use the chain rule to find 23 and as functions of x, y, s and t. Dz B. Find the numerical values of oz and when (s, t) = (5, 4) 32 (5, 4) = (5, 4) =Section 11.5: Problem 3 (1 point) Use the chain rule to find " and , where 7s z = eytan(y), x = 2s + 2t, y = 3t First the pieces: 2 2 75 at 75 at And putting it all together. ay + Dy 08 and z + Dy at\fSection 11.5: Problem 7 {1 pointi Consider The surface F[s,y, z) = 2:333 + stiff} 1 = 1]. Find The following partial derivatives Section 11.5: Problem 9 [1 point) 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 0.02 Volts per second and, as the resistor heats up, the resistance is increasing at [1.02 Ohms per second. When the resistance is 100 Ohms and the current is 0.04 Ampere; at what rate is the current changing? .000208 Amperes per second