8
Problem 8:
Problem 1
Evaluate A. B.
dy dx
4x
when x = 1 if y = 3e -
634.5 678.4
C. D.
5 2 e3x
+ 8 ln 5x
628.3 663.6
E.
685.2
Solve by integration the area bounded by the curves y2 = 4x - 4 and y2 = 2x. A. 4.53 C. 3.45 E. 3.15 B. 1.82 D. 2.67 Problem 9:
Problem 2
In a geometric progression, the sixth term is 8 times the 3rd term and the sum of the seventh and eight terms is 192. Determine the sum of the fifth to eleventh terms, inclusive. A. 2032 C. 2124 E. 2113 B. 2322 D. 2250 Problem 3
A man paid a 10% down payment of P200,000 for a house and lot and agreed to pay the balance on monthly installments for 5 years at an interest rate of 15%. compounded monthly. What was the monthly installment in pesos? A. P42,552.36 C. P42,963.35 E. P42,821.87 B. P42,748.48 D. P42,658.52 Problem 4:
Given f(!) = 5 ln 2 ! - 4 ln 3 !. Determine f’(!). A. !
C.
B. "
D.
E.
1/
2
Problem 10:
The axes of two circular cylinders of equal radii 3 units intersect at right angles. Find their common volume. A. 152 cu.units C. 144 cu.units E. 140 cu.units B. 149 cu.units D. 135 cu.units Problem 11:
A block b lock of monel m onel alloy consists of 70% nickel n ickel and 30% copper. co pper. If it contains 88.2 g of nickel, determine the mass of copper in the block. A. 33.2 kg C. 37.8 kg E. 35.5 kg B. 30.6 kg D. 45.8 kg
If the cost per hour for the fuel required to run a certain ship is proportional to the cube of her speed and is P20 an hour for a speed of 10 knots, and if the other expenses amount to P135 an hour, find the most economical speed at which to run her. A. 13 knots C. 10 knots E. 16 knots B. 15 knots D. 17 knots
The area bounded by the first quadrant of the ellipse 9x2+36y2= 324 is revolved about he y-axis. Find the volume generated. A. 284 C. 256 E. 230 B. 226 D. 214
Problem 5:
Problem 13:
What is the area bounded by the curve y=
and the lines x = 1,
x = 2 and the axis. A. 3 B. 4
E.
C. D.
2 1
0
Problem 12:
It takes 21 hrs. for 12 men to resurface a stretch of road. Find how many men it takes to resurface a similar stretched of road in 50 hrs. and 24 min, assuming the work rate remains constant. A. 3 men C. 4 men E. 7 men B. 5 men D. 6 men
Problem 6:
Problem 14:
A tennis court cou rt measures 24 2 4 m. by 11 m. In the layout layou t of a number numb er of courts an area of ground must be allowed for at the ends and at the sides of each court. If a border of constant width is allowed around each court and the total area of the court and its border is 950 m2, find the width of the borders. A. 3 m. C. 5 m. E. 7 m. B. 4 m. D. 6 m.
Find the volume generated by about the line x - 3 = 0 the area in the second and third quadrants bounded by the curve x2 + y 2 - 9 = 0 and the line x = 0. A. 380 C. 340 E. 400 B. 360 D. 300
Problem 7:
Find the nth term in the following series 2, 6, 10, 14 . . . . . A. 4n - 2 C. 3n + 6 E. 4n + 2 B. 6n - 2 D. 2n + 1
Problem 15:
What is the moment of inertia with respect to the x and y-axis of the area bounded in the first quadrant bounded by the parabola y2 = 4x, the line x = 1 and the x-axis. A. 2.36 C. 1.52 E. 2.87 B. 1.07 D. 1.78
Problem 16:
Problem 25:
A steel girder 8.00 m. long is moved on rollers along a passageway 4.00 m. wide and into a corridor at right angles to the passageway. Neglecting the width of the girder how wide must the corridor be? A. 2.6 m. C. 1.80 m. E. 1.25 m. B. 2.8 m. D. 2.2 m.
A circle is circumscribed about a hexagon. The area outside the hexagon but inside the circle is 15 m2. What is the area of the hexagon in m2? A. 75.48 m2 C. 73.12 m2 E. 78.21 m2 2 2 B. 71.70 m D. 80.58 m
Problem 17:
Problem 26:
Three people P, Q and R contribute to a fund, P provides 3/5 of the total, Q provides 2/3 of the remainder and R provides P8. Determine the total fund. A. P45 C. P60 E. P65 B. P53 D. P57 Problem 18:
The base diameter of a right circular cone is 18 cm. If the lateral area is 516.4 cm2, find its volume in m3. A. 1.3478 m3 C. 2.3125 m3 E. 1.5685 m3 3 3 B. 1.7845 m D. 2.7845 m Problem 19:
If 3 people can complete a task in 4 hours, find how long will it take 5 people to complete the same task, assuming the rate of work remains constant. A. 3.6 hrs. C. 2.2 hrs. E. 1.7 hrs. B. 2.4 hrs. D. 3.2 hrs. Problem 20:
A boy is entitled to 10 yearly endowments of P30000 each starting at the end of the eleventh year from now. Using an interest rate of 8% compounded annually, what is the value of these endowment now? A. P93568.25 C. P93345.15 E. P93656.66 B. P93241.98 D. P93895.25
If y =
3 x
A.
-6 x
B.
C.
3
-6 x
2
- 2 Sin 4x +
- 8 Cos 4x +
3
-6 x
2
e 2 e
e - 6 Cos 4x -
3
2 e
1
+
x
D.
2x
x
dx -6 x
2
+
+
dy
+ ln 5x determine
x
2
- 10 Cos 4x -
x
E.
x
-4 x
- 8 Cos 4x -
3
3
2 e
- 8 Cos 4x -
2 e
+
x
x
1 x
-
1 x
1 x
2
Problem 27:
y = mx + c is the equation of a straight line of slope m and y-axis intercept c. If a line passes through the point where x = 2 and y = 2 and also through the point where x = 5 and y = !, find the equation of the line. A. x = y + 6 C. x = 2y + 6 E. x = y2 + 6 B. x = 3y + 6 D. x = y + 5 Problem 28:
The horizontal base of a regular pyramid is an equilateral triangle 20 m. on each side. If the volume of the pyramid is 531 cu.m., what is its lateral area? A. 308.15 m2 C. 312.25 m2 E. 385.75 m2 2 2 B. 356.35 m D. 325.80 m
Problem 21:
Problem 29:
The first, twelfth and last term of an arithmetic progression are 4, 31 !, 376 ! respectively, determine the number of terms in the series. A. 140 C. 160 E. 170 B. 130 D. 150
A cylinder with an altitude of 15 cm. has a base in the form of a regular octagon inscribed in a square 10 cm. x 10 cm. Find the volume of the cylinder in cu.cm. A. 1448.8 cu.cm. C. 1545.5 cu.cm. E. 1689.6 cu.cm. B. 1354.7 cu.cm. D. 1242.6 cu.cm.
Problem 22:
Problem 30:
Find the volume of the frustum of a regular pyramid if its upper base is 1.5 m. x 1.5 m. square and its lower base is 3.2 m. x 3.2 m. square and its lateral edge is 2.75 m. long. A. 12.15 m3 C. 18.72 m3 E. 14.24 m3 3 3 B. 10.23 m D. 16.23 m
Find the equation of the circle whose center is on the x-axis and which passes through the points (1, 3) and (4, 6). A. x2 + y2 + 14x + 3 = 0 D. x2 + y2 + 14x + 4 = 0 2 2 B. x + y – 12x + 4 = 0 E. x2 + y2 – 14x + 4 = 0 C. x2 + y2 – 14x + 5 = 0
Problem 23:
Problem 31:
A compound curve has the following data: I1 = 28˚, I2 = 38˚, R1 = 380 m., R2 = 220 m. If P.C. is at sta. 20 + 100. Compute the length of the common tangent. A. 162.28 m. C. 166.75 m. E. 180.26 m. B. 170.49 m. D. 184.38 m.
P100000 is deposited at a nominal rate of 7% compounded annually, for 5 years. What would be the difference in the sums at the end of 5 years if the interest were compounded continuously. A. P1652 C. P1748 E. P1451 B. P1562 D. P1885 Problem 32:
Problem 24:
A man buys a house and lot worth 2M pesos if paid in cash. He agreed to pay a down payment of P500,000 and 2 of 1M pesos at the end of one year and the balance at the end of 3 yrs. Determine the amount of this balance if the interest rate is 24%. A. P1,366,351 C. P1,387,215 E. P1,345,685 B. P1,322,852 D. P1,358,748
Find the equations of the tangents to the circle x2 + y2 = 5 which make an angle of 45˚ with x-axis. 10 2
A.
x + y = ± 10
C.
x-y=
B.
x - y = ± 10
D.
x 2 - y 2 = ± 10
E.
x + y = ± 10
Problem 33:
Problem 41:
Find the sum of all numbers between 5 and 250 which are exactly divisible by 4. A. 7748 C. 7894 E. 7963 B. 7862 D. 7808
Using polar coordinates, find the polar equation of the path of a point which is equidistant from the points whose polar coordinates are (2a, 0) and (a, !/2). A.
r=
Problem 34:
Find the equation of the hyperbola with center (1, 3), vertex (4, 3) and end of conjugate axis (1, 1). A. 4x2 - 3y2 – 4x + 50y – 113 = 0 B. 4x2 - 9y2 – 8x + 54y – 113 = 0 C. 4x2 - 6y2 – 6x + 64y – 113 = 0 D. 4x2 - 9y2 – 10x + 58y – 113 = 0 E. 4x2 - 9y2 – 9x + 56y – 113 = 0 Problem 35:
A circular rotonda passes through the three points A(-4, 3), B(2, 1) and C(-2, -5). Determine the radius of this circular rotonda. A. 5.58 C. 6.15 E. 4.27 B. 3.26 D. 4.87
B.
C.
r= r=
3a
D.
2(2 Cos ! - Sin !) 3a 2(Cos ! - Sin !)
E.
r= r=
3a (2 Cos ! - Sin !) 3a 2(2 Cos ! - 2 Sin !)
3a 2(2 Cos 2! - Sin 2!)
Problem 42:
A new bldg. costing P300M, excluding equipment, has an estimated useful life of 40 yrs., with no salvage value. The equipment cost P50M and has an estimated useful life of 15 yrs. with a salvage value of P5M. Using straight line method, what will be the book value of the bldg. and equipment at the end of 10 yrs. A. P245M C. P248M E. P240M B. P232M D. P237M Problem 43:
Problem 36:
The area of a trapezium is 13.5 cm2 and the perpendicular distance between its parallel sides is 3 cm. If the length of one of the parallel sides is 5.6 cm., find the length of the other parallel side. A. 5.8 cm. C. 4.8 cm. E. 3.4 cm. B. 2.5 cm. D. 4.0 cm. Problem 37:
A marquee is in the form of a cylinder surmounted by a cone. The total height is 6 m. and the cylinder portion has a height of 3.5 m. with a diameter of 15 m. Calculate the surface area of material needed to make the marquee assuming 12% of the material is wasted in the process. A. 380.25 m2 C. 350.15 m2 E. 375.56 m2 B. 370.18 m2 D. 393.47 m2 Problem 38:
A Quonset hut 18 m. long has a parabolic cross section. Its base is 12 m. and its height at the center is 6 m. A flat horizontal ceiling 3.70 m. above the base is to be constructed inside the Quonset hut. If the ceiling will consist of wooden boards 25 mm thick, how many cubic meters of ceiling boards will be required assuming that 10% of the materials is wasted during construction? A. 2.365 m3 C. 5.458 m3 E. 3.715 m3 B. 4.542 m3 D. 6.215 m3 Problem 39:
Solve for b from the given equation: 2 log b2 – 3 log b = log 8b – log 4b A. 1 C. 3 E. 5 B. 2 D. 4 Problem 40:
A man cycles 24 km due south and then 20 km due east. Another man, standing at the same time as the first man cycles 32 km due east and then 7 km due south. Find the distance between the two men. A. 20.81 km. C. 22.12 km. E. 18.36 km. B. 25.12 km. D. 16.57 km.
Find the equation of the locus of a point which is at a distance 6 from the point A(5, 3, 2). A. x2 + y2 + z2 – 10x – 6y – 4z + 3 = 0 B. x2 + y2 + z2 – 10x – 6y – 4z + 4 = 0 C. x2 + y2 + z2 – 10x – 6y – 4z + 2 = 0 D. x2 + y2 + z2 – 10x – 6y – 4z + 5 = 0 E. x2 + y2 + z2 – 10x – 6y – 4z + 1 = 0 Problem 44:
A vertical summit curve has its highest point of the curve at a distance 48 m. from the P.T. The back tangent has a grade of + 6% and a forward grade of – 4%. The curve passes thru point A on the curve at station 25 + 140. The elevation of the grade intersection is 100 m. at station 25 + 160. Compute the length of curve. A. 125 m. C. 120 m. E. 115 m. B. 135 m. D. 130 m. Problem 45:
A piece of thin card board in the form of a sector of a circle of radius 36 cm. is rolled into a cone. Find the volume of the cone if the angle of the sector is 60˚. A. 1126.2 cu.cm. C. 1338.3 cu.cm. E. 1545.5 cu.cm. B. 1878.5 cu.cm. D. 1456.8 cu.cm. Problem 46:
A rectangular piece of metal having dimensions 4 cm. by 3 cm. by 12 cm. is melted down and recast into a pyramid having a rectangular base measuring 2.5 cm. by 5 cm. Calculate the perpendicular height of the pyramid. A. 26.65 cm. C. 45.75 cm. E. 40.36 cm. B. 34.56 cm. D. 55.58 cm. Problem 47:
Two similar cylinders have pentagonal bases. The sides of the base of the bigger cylinder are 5 cm., 6 cm., 8 cm., 9 cm. and 3 cm. long. The shortest side of the base of the smaller cylinder is 1 cm. If the altitude of the smaller cylinder is 10 cm., what is the total lateral area in sq.cm. A. 121.25 cm2 C. 130.52 cm2 E. 103.30 cm2 B. 112.32 cm2 D. 110.23 cm2
Problem 48:
Problem 58:
A cylindrical tank of diameter 2 m. and perpendicular height 3 m. is to be replaced by a tank of the same capacity but in the form of a frustum of a cone. If the diameters of the ends of the frustum are 1.0 m. and 2.0 m. respectively, determine the vertical height required. A. 6.02 m. C. 5.14 m. E. 3.36 m. B. 4.91 m. D. 7.01 m.
Differentiate with respect to x if y = 5 e3x. A. 15 e3x C. 14 e3x B. 13 e3x D. 12 e3x
Problem 49:
The sides of a triangle are 45 m. and 55 m. long. If its area is 785.48 m2. Find the sum of the sides. A. 123 m. C. 118 m. E. 130 m. B. 135 m. D. 132 m. Problem 50:
Calculate the area of a regular octagon if each side is 20 mm and the width across the flats is 48.3 mm. A. 1825 mm2 C. 1932 mm2 E. 1886 mm2 2 2 B. 1748 mm D. 1645 mm Problem 51:
A spherical sector is cut from a sphere whose radius is 12 cm. Find its volume if its central angle is 20˚. A. 60 cu.cm. C. 55 cu.cm. E. 50 cu.cm. B. 57 cu.cm. D. 52 cu.cm. Problem 52:
If f(x) = 4x5 – 2x3 + x – 3, find y”(x). A. 60x3 – 12x C. 80x3 – 10x 3 B. 80x – 15x D. 80x2 – 12x
E.
80x3 – 12x
Problem 53:
The perimeter of triangle ABC = 180 m. A = 46.567˚, B = 104.478˚, what is the dimension of the side opposite the biggest angle? A. 67 m. C. 72 m. E. 80 m. B. 63 m. D. 75 m. Problem 54:
E.
10 e3x
Problem 59:
The area of a circle inscribed in a nonagon is 76 m2. What is the area of the nonagon? A. 75.5 m2 C. 82.3 m2 E. 79.2 m2 2 2 B. 67.4 m D. 85.7 m Problem 60:
A circle having an area of 452 m2 is cut into two segments by a chord which is 6 m. from the center of the circle. Compute the area of the biggest segment. A. 375.42 m2 C. 312.24 m2 E. 363.68 m2 B. 350.33 m2 D. 332.15 m2 Problem 61:
Determine the area enclosed by the curve y = x3 + 2x 2 – 5x – 6, the x-axis between x = -3 and x = 2. A. 26.35 sq.units C. 15.48 sq.units E. 32.52 sq.units B. 23.69 sq.units D. 21.08 sq.units Problem 62:
The upper end of a 3 m. pipe leans against a vertical wall, while the lower end is on a level concrete pavement extending to the wall. The lower end slides away at a constant rate of 2 cm/s. How fast is the upper end moving down on the wall in cm/s when the lower end is 2 m. away from the wall? A. - 3.68 cm/sec. C. - 2.36 cm/sec. E. - 2.05 cm/sec. B. - 0.45 cm/sec. D. - 1.79 cm/sec. Problem 63:
The velocity V of a body t seconds after a certain instant is (2t2 + 5) m/s. How far will it move from t = 0 to t = 4 sec. A. 74.15 m. C. 62.67 m. E. 65.85 m. B. 70.36 m. D. 60.23 m. Problem 64:
The volume of frustum of a sphere with two bases is equal to 159! cu.m. If the radii of the bases are 4 m. and 5 m. respectively. Compute the radius of the sphere. A. 3.12 m. C. 6.85 m. E. 4.25 m. B. 7.85 m. D. 5.48 m.
A pyramid has a rectangular base 3.60 cm. by 5.40 cm. Determine the volume of the pyramid if each of its sloping edge is 15 cm. A. 96.25 cm3 C. 94.87 cm3 E. 98.65 cm3 B. 95.68 cm3 D. 97.65 cm3
Problem 55:
Problem 65:
If y = 3x4 + 2x3 – 3x + 2, find A. B. C.
36x2 + 10x 36x2 + 13x 36x2 + 11x
As a man walks across a bridge at a speed of 1.5 m/s, a boat passes directly beneath him at a speed of 3 m/s. The bridge is 9 m. above the water. How fast in m/s are the boat and the man separating 3 seconds later. A. 2 m/s C. 1.8 m/s E. 2.5 m/s B. 4 m/s D. 3.2 m/s
d3 y d x3 C. D.
36x2 + 12x 36x2 + 15x
Problem 56:
Problem 66:
A buoy consists of a hemisphere surmounted by a cone. The diameter of the cone and hemisphere is 2.5 m. and the slant height of the cone is 4 m. Determine the volume and surface area of the buoy. A. 14.40 cm3, 25.53 cm2 C. 16.78 cm3, 24.86 cm2 B. 13.52 cm3, 22.48 cm2 D. 12.52 cm3, 23.48 cm2 3 2 C. 15.68 cm , 20.47 cm
Problem 67:
Problem 57:
How many diagonals are there in a dodecagon? A. 50 C. 56 B. 58 D. 54
An open cylindrical tank with a radius of 0.5 m. and a height of 2 m. is full of oil. It is gradually tilted until half of its bottom area is exposed. Find the volume of oil left inside the tank in cu.m. A. 0.33 m3 C. 0.12 m3 E. 0.65 m3 B. 0.85 m3 D. 0.58 m3
Evaluate the following limits: lim E.
52
x!0
A. B.
1 3
C. D.
2 0
tan x - x x - sin x
E.
4
Problem 78:
Problem 68:
Evaluate the integral A. B.
1/2 x2 + ln x + C 3/2 x2 + ln x + C
! (
3x2 - 1
C. D.
x
) dx
5/2 x2 + ln x + C 3/4 x2 + ln x + C
E.
1/3 x2 + ln x + C
Problem 69:
Evaluate the integral A. 5 B. 10
x +C 2x + C
Problem 79:
!
5 dx x 2
C. 10
x + C
D. 10
x +C
E.
x +C
Problem 70:
Determine the area enclosed by y = 2x + 3, the x-axis, and ordinates x = 1 and x = 4. A. 18 sq.units C. 24 sq.units E. 22 sq.units B. 15 sq.units D. 20 sq.units Problem 71:
A circle with a diameter of 8 cm. is inscribed in a circular sector with a central angle of 80˚. What is the area of the sector? A. 72.96 cm2 C. 83.16 cm2 E. 80.72 cm2 B. 75.36 cm2 D. 66.68 cm2 Problem 72:
In a batch of 45 lamps there are 10 faulty lamps. If one lamp is drawn at random. Find the probability of it being satisfactory. A. 0.7778 C. 0.1525 E. 0.3652 B. 0.5456 D. 0.7845 Problem 73:
Find the horizontal asymptote of the curve y = A. B.
y2 – 2 = 0 y+3=0
The perpendicular offset distance from point A on a simple curve to Q on the tangent line is 64 m. If the distance from the P.C. to Q on the tangent is 260 m. Compute the radius of the simple curve. A. 525.36 m. C. 512.12 m. E. 560.13 m. B. 587.15 m. D. 541.96 m.
C. D.
y–3=0 y+2=0
E.
y–2=0
Problem 74:
A square having an area of 48 sq.cm. is inscribed in a circle which is inscribed in a hexagon. Compute the area of the hexagon. A. 77.42 sq.cm. C. 86.15 sq.cm. E. 83.23 sq.cm. B. 72.05 sq.cm. D. 92.75 sq.cm.
The angle of depression of a ship viewed at a particular instant from the top of a 75 m. vertical cliff is 30˚. The ship is sailing away from the cliff at this instant at constant speed and 1 minute later its angle of depression from the top of the cliff is 20˚. Determine the speed of the ship in kph. A. 2.36 kph C. 3.18 kph E. 6.35 kph B. 4.57 kph D. 5.68 kph Problem 80:
Solve for x from the equation: Log (x – 1) + log (x + 1) = 2 log (x + 2) A. - 7/4 C. - 5/4 E. - 1/4 B. - 3/4 D. - 9/4 Problem 81:
Two aircraft leave an airfield at the same time. One travels due north at an average speed of 300 kph and the other due west at an average speed of 220 kph. Calculate their distance apart after 4 hrs. A. 1235 km. C. 1312 km. E. 1488 km. B. 1612 km. D. 1526 km. Problem 82:
Boyles law states that for a gas at constant temperature, the volume of a fixed mass is inversely proportional to its absolute pressure. If a gas occupies a volume of 1.5 m3 at a pressure of 200 x 10 3 Pascals. Determine the volume when the pressure is 800 x 103 Pascals. A. 0.375 m3 C. 0.235 m3 E. 0.735 m3 B. 0.558 m3 D. 0.878 m3 Problem 83:
A car has a mass of 1000 kg. A model of the car is made to a scale of 1 to 50. Determine the mass of the model if the car and its model are made of the same material. A. 0.002 kg C. 0.005 kg E. 0.007 kg B. 0.008 kg D. 0.004 kg Problem 84:
Problem 75:
This sides of a square lot having an area of 2.25 hectares were measured using a 100 m. tape that was 0.04 m. too short. Compute the error in the area in sq.m. A. 20 sq.cm. C. 15 sq.cm. E. 18 sq.m. B. 17 sq.cm. D. 16 sq.cm. Problem 76:
What is the curved surface area of a spherical wedge having a radius of 3.5 m. and a central angle of 0.65 radians. A. 12.3 m2 C. 20.5 m2 E. 10.5 m2 2 2 B. 15.9 m D. 18.2 m Problem 77:
Find the diameter of the circle that maybe inscribed in a triangle whose area and perimeter are 212 sq.m. and 136 m. respectively. A. 6.24 m. C. 7.52 m. E. 4.15 m. B. 5.23 m. D. 8.66 m.
A curve having an equation of y = ax3 + bx2 + cx will have a slope of 4 at its point of inflection (-1, 5). Find the value of a. A. 3 C. 2 E. 0 B. 4 D. 1 Problem 85:
A model of a boiler is made having an overall height of 75 mm corresponding to an overall height of the actual boiler of 6 m. If the area of metal required for the model is 12500 mm2, determine the area of metal required for actual boiler in square meters. A. 50 m2 C. 70 m2 E. 90 m2 B. 60 m2 D. 80 m2 Problem 86:
PQR is an equilateral triangle of side 4 cm. When PQ and PR are produced to S and T, respectively, ST is found to be parallel with QR. If PS is 9 cm., find the length of ST. A. 8 cm. C. 7 cm. E. 9 cm. B. 10 cm. D. 6 cm.
Problem 87:
Problem 94:
A line was measured witha 50 m. tape. There were 2 tallies, 8 pins, and the distance from the last pin to the end of the line was 2.25 m. Find the length of the line in meters? A. 1563.38 m. C. 1215.58 m. E. 1312.78 m. B. 1178.43 m. D. 1402.25 m.
If f(t) = 4 ln t + 2, evaluate f;(t) when t = 0.25. A. 16 C. 14 B. 15 D. 17
Problem 88:
Water flows at the rate of 2000 cc/s into a vertical cylindrical tank 120 cm. in diam. and 6 m. high. How fast is the water level rising in cm/s. A. 0.177 cm/s C. 0.875 cm/s E. 0.265 cm/s 0.458 cm/s 0.365 cm/s B. D.
The probability that component A will operate satisfactorily for 5 years is 0.80 and that B will operate satisfactorily over that same period of time is 0.75. Find the probability in a 5 year period if both components operate satisfactorily. A. 0.25 C. 0.30 E. 0.52 B. 0.60 D. 0.85 Problem 89:
Differentiate with respect to x if y =
2 2x
7e
A.
-6 2x
C.
7e
B.
-2 2x
-5
E.
2x
7e
D.
7e
-4
E.
18
Problem 95:
Problem 96:
A solid has a circular base of radius 20 cm. Find the volume of the solid if every plane section perpendicular to a certain diam. is an equilateral triangle. A. 17,123 cm3 C. 18,215 cm3 E. 18,475 cm3 B. 18,628 cm3 D. 18,754 cm3 Problem 97:
2x
7e
-3 2x
7e
Problem 90:
A batch of 100 capacitors contains 73 which are within the required tolerance values, 17 which are below the required tolerance values and the remainder are above the required tolerance values. Determine the probability that when randomly selecting a capacitor and then a second capacitor if both are within the required tolerance values when selecting with replacement. A. 0.2565 C. 0.4785 E. 0.745 B. 0.8785 D. 0.5329
The probability of a component failing in one year due to excessive temperature is 0.05, due to excessive vibration is 0.04 and due to excessive humidity is 0.02. Determine the probability that during one year period, a component fails due to excessive temperatures and excessive vibration. A. 0.045 C. 0.002 E. 0.112 B. 0.085 D. 0.012 Problem 98:
Determine the equation of the radical axis of the circles x2 + y2 - 18x - 14y + 121 = 0 and x2 + y2 - 6x + 6y + 14 = 0. A. 12x + 20y – 107 = 0 D. 12x – 20y + 107 = 0 B. 12x + 20y + 107 = 0 E. 12x – 20y + 105 = 0 C. 12x – 20y – 107 = 0
Problem 91: Problem 99:
Differentiate the following equation f(t) =
4 5t
3e
A.
-20 5t
C.
3e
B.
-22 5t
3e
-25 5t
3e
D.
E.
-28 5t
3e
-30 5t
Find the point on the curve y2 = 8x which is nearest to the external point (4, 2). A. 1 C. 3 E. 5 B. 2 D. 4 Problem 100:
3e
Problem 92:
A wood man chops halfway through a tree of diam. 1 m., one face of the cut being horizontal, the other inclined at 45˚ with the horizontal. Find the volume of the wood in cu.m. A. 0.067 m3 C. 0.028 m3 E. 0.083 m3 3 3 B. 0.055 m D. 0.048 m Problem 93:
A set out to walk at the rate of 4 km/hr. After he had been walking 2 " hours, B set out to overtake him and went 4 ! km the first hour, 4 " the second hour, 5 km the third hour, and so on, gaining a quarter of a km every hour. In how many hours would he overtake A? A. 7 hrs. C. 9 hrs. E. 5 hrs. B. 8 hrs. D. 6 hrs.
Determine the area bounded by the curve y = Sin x and the x-axis between x = 2! and x = 3!. A. 3 C. 2 E. 0 B. 4 D. 1
