Please provide a neat solution. You may use a calculator technique but explain the concepts or formula you will use. Thank you.

Items 67-77:

50. Find the volume (in cubic units) generated by rotating a circle x? + y? + 0x + 4y + 12 = 0 about the y-axis. A. 39.48 C. 59.22 B. 47.23 D. 82.11 60. The focus of the parabola y? = 4x is at A. (4. 0) B. (0. 4) C. (3. 0) D. (0, 3) 61. Find the equation of the directrix of the parabola y = 10x A x=2 C. x=4 B. x=-2 D. x= 4 62. A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold? A. 40 B. 35 C. 45 D. 38 63. What is the value of each interior angle of regular pentagon? A 75 B. 27/5 C. 72 D. 31/5 64. A cubical container that measures 2 m on a side is tightly packed with eight balls and is filled with water. All eight balls are in contact with the walls of the container and the adjacent balls. All of the balls are the same size. What is the volume of water in the container? A. 0.38 m C. 3.8m B. 25m D. 4.2 m 65. Which number has four significant figures? A. 0 0014 C. 0.141 B. 0 01414 D. 1.4140 68. The salary of an employee's job has five levels, each one 5% greater than the one below it. Due to circumstances. the salary of the employee must. Be reduced from the top (fifth) level to the second level, which results in a reduction of P 2,440.00 per month. What is the employee's present salary per month? A. P 8,800.00 C. P 13,800 B. P 11.400.00 D. P 18,000 67. What is the rank of the matrix A? A= A O B. 1 C. 2 D. 3 68. Determine the values of x, and x, that satisfies the following linear system A X =4; x=-2 C. X1 = -2; x2 =4 B. x = 2; x2 = -4 D. x1 =-4; x2 = 2 60. What is the resultant, R, of the vectors Fi = 4 + 7j + 6k, F= = Qi + 2j + 1 1k and Fa = 5i - 3j - 8k? A. 18i + 6 + 9k C. 18i + 12j + 25k B. - 181 -6j -9k D. 21j 70. Simplify the expression (A x B)-C, given A = 3i + 2j, B = 2i + 3j + k and C = 5i + 2k. A D C. 601 + 24k B. 20 D. 5i + 2k 71. One fair die is used in a dice game. The player wins P 10 if he rolls either a 1 or a 6. He loses P 5 if he tums up any other face. What is the expected winning for one roll of the die? A O C. P 5100 B. P3.33 D. P 6.6772. An um contains 4 black balls and six white balls. What is the probability of getting one black ball and one white ball in two consecutive draws from the um without replacement? A. 0 040 C. 0.27 B. 024 D. 0.53 73. What is the exponential form of the complex number 3 + 4i? A. e raised to 53.1"i B. 5e raised to 53. 19i C. Se raised to 128.9i D. 7e raised to 53.1'i 74. What is the product of the complex numbers 2 - 2j and v32 emu? A. 16 C. 10emmi4 B. j16 D. 16(1 -i) 75. What is the rationalized value of the complex quotient? (6 + j2.5) / (3 + 14) A. - 0.32 + j0.86 C. 1.1-j0.68 B. 0.32-10.68 D. - 1.7 + j1.1 76. Water is pouring at a varying rate into a swimming pool that is initially empty. Aftert hours, there are t + vt liters in the pool. At what rate is the water pouring into the pool when t = 9 h? A 1/6 L/h C. 1Lh B. 1/2 L/h D. 7/6 /h 77. A spherical balloon is filled with air at a rate of 1 m'/'s. Compute the time rate of change of the surface area of the balloon at the instant the balloon's volume is 113.1 m. A 0.67 mil's C. 3.1 m/s B. 1.7 mal's D. 3.7 m/'s 78. Compute the limit lim +2 I-40X-2 AO B. 1 C. 2 D. CO 70. Simplify the following expression lim x - 16 3-4 X-4 A. O B. B C. 12 D. 16 80. What is the Laplace transform of e -? A. 1/ (s+8) C. e-6. B. 1/ (5-6) 81. How many numbers between 20 and 1,058 are exactly divisible by 14? A 73 B. 74 C. 75 D. 76 82. A can do a piece of work alone in 2 days, B alone in 3 days, and C alone in 6 days. If they work together. how many days would it take them to finish the work? A 1.50 days C. 0.5 day 1.60 days D. 1 day 83. A chord measuring 1.25 m is 0.85 m from the center of a circle. Find the area of the circle. A. 5.60 sq. m C. 2.55 sq, m B. 4 34 sq. m D. 8.24 sq m 84. Find the general solution of the differential equation dyldx + yx = 1 A 2y= X+ C C. xy = 2x3 + C B. 2xy= x+ C D. xy = 2x + C 85. A card is drawn from an ordinary deck of 52 cards. Find the probability that the card is a face card or heart. A 1/18 B. 3/52 C. 11/26 D. 1/4 38. What is the probability of getting 7 or 11 when a pair of dice is thrown? A. 2/9 B. 1/6 C. 1/18 D. 3/8 87. If the surface area of the sphere is 2.123.72 sq. cm., find its volume. A. 11,404.04 cu. cm. B. 9 202.77 GUL Cm. C. 5,575.28 Gu. cm. D. 7.238.23 cu Cm