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Solve the problem. A boat is towed toward a doclc by a cable attached to a winch that stands '15 Ft above the water level [see gure}. Let B be the angle of elevation of the winch and let 2 be the length of the cable as. the boat i5 towed toward the dock. Compute E when z=33ft (31:19 E = {1.51131 '3' E = 43.41952 '3 g = -o.ooa55 O E = oooots dz Find the limit. lim (e 5/X - 6x) x/2 X-0 O O 0 O 2.5 O 2.5Evaluate the integral. dx x/ 16 2 -7 O sec 7 7 =1 7 * +C O | sec-1 | 4x - 7| + C O 7 sin JH A. x +C O sec-1 |4 x | + CUse logarithmic differentiation to find the derivative of y. 5 x(x - 4) y x3+3 O (In x + In(x - 4) - In(x3 + 3)) O 1 1 3x2 + X X - 4 x3 + 3 O 1 5 (x(x - 4) 1 3x2 + x 3+ 3 X X - 4 x3 + 3 5 (x(x - 4) 1 3x2 Un + 3 + 3 X X - 4 3+3Solve the problem. How long will it take for prices in the economy to double at a 7% annual inflation rate? Round the answer to the nearest hundredth. O 23.45 yr O 10.24 yr O 9.01 yr O 16.24 yrFind the derivative of y with respect to the independent variable. y = 2 x O 2X O 2% In 2 O 2* In x O x In 2Solve the problem. The population of a small country increases according to the function B = 1,400,000e .USt, where t is measured in years. How many people will the country have after 9 years? O 2,195,637 people O 1,117,911 people O 3,945,736 people O 485,502 peopleUse logarithmic differentiation to find the derivative of y. (3x + 1)(x + 3)2 (x3 + 6)(x+7) O 5 (In(3x + 1) + 2In(x + 3) - In(x3+ 6) - In(x + 7)) O 1 5 (3x + 1)(x + 3)2 3 2 3x2 1 + (x3 +6)(x +7) 3x + 1 x + 3 x3+6 X+ 7 O 5 5 (3x + 1 )(x + 3)2 3 2 3x2 1 + (xX3+ 6)(x +7) 3x + 1 x+ 3 *3 +6 X+7 O 3 2 3x2 + 3x + 1 x + 3 x3 + 6 X+ 7Use logarithmic differentiation to find the derivative of y. y = COS X 4/X+ 1 O cos x /x + 1 Incosx + -In(7x +1) O 7 cos x 17x+ 1 -tanx + 2(7x + 1) O 1 7 COS XAN/x+ 1 + sinx . Cos 7x + 1 O -14-tanx + 5-tanx 7x + 2Use logarithmic differentiation to find the derivative of y. y = x(x + 8)(x +9) O x(x + 8)(x + 9)(Inx + In(x + 8) + In(x +9)) O 1 O 1 + + X X + 8 X+9 C 1 1 1 x(x + 8)(x +9) + + X X + 8 X+9\fEvaluate the integral. Ge(6 sin 5x) dx sec 5x O (6 sin 5x) + C 6 In( sec 5x) + C O (6 sin 5X) + C O In(sec 5x) + CEvaluate or simplify the given expression. cost2 sin -1 x) O 1 -x 2 O 2 x 2 + 1 01 O 1 -2x2Evaluate the integral. gcost sin t dt O 971/2-1 In 9 0 8 O -8 In 9 O In 9Provide an appropriate response. Find an equation of the line tangent to y = x Col * at the point x = 1. O y = x cot 1 + 1 - cot 1 O y = x cot 1 - 1 - cot 1 O y = x cot 1 - 1 + cot 1 O y = x cot 1 + 1 + cot 1Solve the problem. In the formula A = le , A is the amount of radioactive material remaining from an initial amount I at a given time t and k is a negative constant determined by the nature of the material. A certain radioactive isotope has a half-life of approximately 1,850 years. How many years would be required for a given amount of this isotope to decay to 55% of that amount? O 2,131 yr O 1,541 yr O 832.5 yr O 1,596 yrEvaluate the integral. 12 xax
