問題一覧
1
Determine the nature of the surface whose equation is 2 (x square) - 3 (y square) +( z square) 8x + 16y - 2z = 30
Hyperboloid
2
Find the polar moment of inertia of the area of a circle of radius 2 cm with respect to its center.
8 pi
3
How many kg. of cream containing 25 percent butter fat should be added to 50 kg of milk containing one percent butter fat to produce milk containing 2 percent butter fat?
2.174
4
The probability of getting at least two heads when a fair coin is tossed four times is
11/16
5
Find the angle in degrees between the vectors joining the origin to point P (1, 2, 3) and P( 2, - 3 , -1). Use space vector.
120
6
Determine the simplified form of sin 2B/ (1 - cos 2B)
cot B
7
Gravity causes a body to fall 16.1 feet in the 1 second, 48.3 ft in the 2rd second, 80.5 ft in the 3rd second, and so on. How far did the body fall during the 10th second?
305.9 ft
8
Determine the radius of the sphere whose equation is: x ^ 2 + y ^ 2 + z ^ 2 - 2x + 8y + 16z + 65 = 0
4 units
9
With a throw of 3 dice, what is the probability of getting a 9 or an 11?
52/216
10
The second derivative of the function f(x) is-f(x). What is a characteristic of this function
trigonometric
11
A water tank is shaped in such a way that the volume of water in the tank is V = 2y ^ 3 / 2 cu. in. when its depth is y inches. If water flows out through a hole at the bottom of the tank at the rate of 3 sq. rt. of y cu. in. / min, at what rate does the water level in the tank fall?
1 in/min
12
Solve (x + y) dy = (x - y) dx
x^2 - 2xy - y^2 = C
13
4 yards is how many inches
144
14
The equation {z ^2} = 4 represents which of the following curve?
Hyperbola
15
A steel girder 8m long is moved on rollers angle to the passageway 4m wide into a corridor at right angle to the passageway. Neglecting the width of the girder, how wide must the corridor be?
1.8 m
16
A railroad is to be laid-off in a circular path. What should be the radius if the track is to change direction by 30° at a distance of 157.08m?
300 m
17
The area enclosed by the ellipse 4x^2 + 9y^2 = 36 is revolved about the line x = 3 What is the volume generated
355.3
18
A ball is dropped from a height of 18m. On each rebound it rises 2/3 of the height from which it last fell. What is the distance has it traveled at the instant it strikes the ground for the 5th time?
75.78 m
19
A group consist of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n.
100
20
Two circles with different radius but with the same center are called _____ circles.
Concentric
21
From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their mother's voice. Find the variance of x.
1.8
22
From past experience, it is known 90% of one-year old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Find the probability that all 20 children recognize their mother's voice
0.122
23
Find the minimum distance from the point (4, 2) to the parabola y ^ 2 = 8x
2 sq. rt of 2
24
Find all values of z for e ^ n * (4z) = 1
πi/8 + kπi/2
25
One end of a 32m ladder resting on horizontal plane leans on a vertical wall. Assume the foot of the ladder to be pushed towards the wall at the rate of 2m/min. How fast is the top of the ladder rising rising when its foot is 10m from the wall?
0.658 m/min
26
Find the moment of inertia of the area bounded by the parabola y ^ 2 = 4x and the line x = 1, with respect to the x axis.
2.13
27
Find the length of the arc described by the parabola x ^ 2 = 4y from x = - 2 to x = 2
4.59
28
Two hundred single-sports athletes were cross-classified according to gender as follows:
Swimmer Runner Cyclist
Male 25 60 25
Female 20 50 20
What is the probability that the athlete is male or a swimmer or both?
0.550
29
Find the area enclosed in the second and third quadrants by the curve x = t^2 - 1 y= 5t^3 (t^2 -1)
8/7
30
The diameter of a circle is 10 cm and with its chord decreasing at the rate of 1cm/min. Determine the rate by which the arc subtended by the chord is changing when the chord is 8 cm long.
- 1.67 cm/min
31
Find the volume of the solid common between intersecting cylinders with radius of 3 ft.
144
32
A ranger in tower A saw a flash fire south of him while a ranger in tower B 20km east of tower A saw the flash fire with a bearing of 540° 15°W Find the distance of the flash fire from tower A.
23.62 km
33
A number is divided into two parts such that when the greater part is divided by the smaller, the quotient is 3 and the remainder is 5. Find the smaller number if the sum of the two numbers is 37
8
34
An audience of 450 persons is seated in a row having the same number of persons in each row. If 3 more persons seat in each row, it would require 5 rows less to sear the audience. How many rows were there originally?
30
35
Find the angle in mils subtended by a line 10 years long at a distance of 5000 yards.
2.04 mils
36
If 3x^2 is multiplied by the quantity 2x^3y raised to the 4th power, what would this expression simplify to?
48x^14y to the 4th power
37
Identify the curve r = a + b cos theta
Limacon
38
An open cylinder trough is constructed by bending a given sheet of tin and breadth 2a. Find the radius of the cylinder of which the trough forms a part when the capacity of the trough is a maximum.
0.637a
39
Solve the linear equation: d/dx (y) + y / x = x^2
xy = x^4/4 + C
40
Alex bought 400 hot dogs for the school pic. If they were contained in packages of 8 hot dogs, how many total packages did he buy?
50
41
A bus leaves Manila at 12 noon for Baguio 250 km away, travelling at an average of speed of 55 kph. At the same time, another bus leaves Baguio for Manila travelling at an average speed of 65 kph. At what time will they meet?
2:05 PM
42
A politician analyst asked a group of people how they felt about two political policy statements. Each person was to respond A (agree), N(neutral) and D(disagree) to each NN, ND, DA, AN, .... DD. Assuming each response combination is equally likely, what is the probability that the person being interviewed agrees with exactly one of the two political policy statements?
4/9
43
Bonnie has twice as many cousins as Robert. George has 5 cousins which is 11 less than Bonnie has. How many cousins does Robert have?
8
44
A tank initially holds 100 gal of salt solution in which 50 lbs. of salt has been dissolved. A pipe fills the tank with brine at the rate of 3gpm containing 2 lbs. of dissolve salt per gallon. Assuming that the mixture is kept uniform by stirring a drain pipe draws out of the tank the mixture of 2gpm. Find the amount of salt in the tank at the end of 30 minutes
171.24 lbs
45
It is one of the eight divisions of three-dimensional coordinates system.
Octants
46
Find the area of the largest rectangle that can be inscribe in an ellipse x ^ 2 + 4y ^ 2 = 4
4
47
How many positive real solutions are there in the polynomial: x ^ 4 - 4x ^ 3 + 7x ^ 2 - 6x - 18 = 0
3 or 1
48
A military supply truck contains 3 tons of food. If a soldier eats 12 ounces for breakfast, 18 ounces each for lunch and dinner, how many soldiers can be fed by the supply for 10 days?
200
49
If f(x) = 10^x + 1 then f(x + 1) - f(x) is equal to
9(10^x)
50
Four radars are tracking an asteroid. If the probability of tracking success is 90%, find the probability of at most 3 successes
0.3439
51
Find the equation of the circle that passes through the vertex and end points of the latus rectum of the parabola y ^ 2 = 8x
x ^ 2 + y ^ 2 = 10x
52
Evaluate the limit of z^2/(z^4 + z + 1) as z approached e^(π/4)i
sq.rt. of 2(1+i)/2
53
Find the volume of a cube having its two faces laid in the planes 2x - y + 2z - 3 = 0 and 6x - 3y 6z + 8 = 0 0 = angle E- angle+ angle A
4913/729
54
Compute log(3 - 2i)
0.5570 + 0.2554i
55
Water is running out a conical funnel at the rate of 1 cu. in./sec. If the radius of the base of the funnel is 4 in, and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in, from the top.
- 1/9π in/s
56
A steel ball is 12°C cools in 20 min to 80°C in a room 25°C Find the temperature of the ball after half an hour.
66.85°C
57
Find the unit vector which is orthogonal to 9i + 9i and 9i + 9k
(i - 1 - k)/sq.rt. of 3
58
A ball bounces 2/3 of the altitude from which it falls is dropped from a height of 18 ft., how far will it travel before coming to rest?
90 ft
59
The line passing through the focus and perpendicular to the directrix of parabola is called
axis
60
A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the success of the new product. The survey showed 40% of the consumers had seen an advertisement for the new soup, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. If a randomly selected consumer has seen an advertisement for the new soap, what is the probability that this consumer has tried the new soap
37.5%
61
Find the volume generated by revolving the area bounded by y ^ 2 = 12x and x = 3 about the line x=3.
181
62
Solve the equation (x²y-2)+(x+2xy-5) i = 0.
x = 1, y = 2
63
Describe the locus represented by l z - i |=2
circle
64
Evaluate Integrate √(1 - cos x) dx
2√2 cos x + C
65
Find the equation of the bisector of the pair of acute angles formed by the line 4x + 2y = 9 and 2x - y = 8
8x - 25 = 0
66
Solve the particular solution of d/dx (y) - (3y)/x = x ^ 3 y(1) * d * 4
y = x^4 + 3x^3
67
Determine the equation of the line normal to the graph x^2 + 3xy + y^2 = 5 at the point (1, 1).
x - y = 0
68
Express decimally: Fifty-Eight millionth
0.000058
69
From a hill 600 ft. high, the angles of depression to the bases in opposite directions are 42" and 19 deg * 23' respectively. Find the length of the proposed tunnel through the bases.
2,371.74 ft.
70
Find the distance of the directrix from the center of an ellipse if its major axis is 10 and its minor axis is 8.
8.3
71
In the REE Board examinations, the probability that an examinee will pass in each subject is 0.75. What is the probability that an examinee wil pass at least two subjects?
0.84375
72
An ellipse with major axis 16 and minor axis 8 is revolved about its minor axis. Find the volume of the solid generated
1024 π/3
73
An airplane flies at a speed of 240 mph in still air S30°W with a wind speed of 40 mph due west. What is the new bearing?
S38°W
74
Bill, Bob, and Barry are hired to paint signs. In 8 hours, Bill can paint 1 sign, Bob can paint 2 signs, and Barry can paint 1 1/3 signs, They all come to work the first day, but Barry doesn't like the job and quits after 3 hours. Bob works half an hour longer than Barry and quits. How long will it take Bill to finish the two signs they were supposed to paint?
1 1/2 hrs
75
Hotels, like airlines, often overbook, counting on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservations will not be used if four reservations are made, what is the chance fewer than two will cancel
0.8192
76
Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft. high if the height is increasing at 2 in/min.
130, 288.13 in/min
77
Evaluate: lim (2 - x) ^tan Dx/2
s^2/D
78
Liza thought she had the exact money to buy 10 chocolate bars. However, the price per bar had Increased by 50 centavos. Consequently, she was able to buy only 8 bars and had P2 left. How much money did Liza have
30
79
Find the maximum value of 3^sin 3x.
3
80
If the general equation of the conic is A * x ^ 2 + Bxy + C * y ^ 2 + Dx + Ey + F = 0 and B ^ 2 - 4AC > 0 then the conic is
hyperbola
81
Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486.
844
82
A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least P50. A random sample of 20 alumni is selected. What is the probability that less than 17 alumni will make a contribution of at least P50
0.589
83
Find the equation of the normal line to x ^ 2 + y ^ 2 = 1 at the point (2, 1).
x = 2y
84
Jun rows his banca across a river at 4 km/hr. How lorig will it take Jun to cross the river?
3.78 min
85
The difference between six times the quantity 6x + 1 and three times the quantity x - 1 is 108. What is the value of x?
3
86
Michael walks to school. He leaves each morning at 7:32 A.M. and arrives at school 15 minutes later. If he travels at a steady rate of 4.5miles/hour. What is the distance between his home and school?
1.1
87
The time a student spends learning a computer software package is normally distributed with a mean of 8 hours and standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends less than 6 hours learning a software package?
0.09
88
What is the smallest positive value for x where y = sin 2x reaches its maximum
D/4
89
Find the vertex of the parabola x ^ 2 = 4y
(0,0)
90
When the energy/hour required in driving a boat varies as the cube of the velocity, find the most economical rate /hour when going against a current of 4kph.
6 kph
91
After paying a commission of 7% of the sale price to his broker, Tess receives P 103,000 for his car. How much was the car sold?
P110,753
92
Find an equation of the parabola with vertex (-1,-2) latus 12, opens downward.
x ^ 2 + 2x + 12y + 25 = 0
93
The towns are located near the straight shore of the lake. Their nearest distances to the point in the shore are 1km and 2 km respectively, and these points on the shore are 6 km apart. Where the fishing port should be located to maximize the total amount of paving necessary to build a straight road from each town to the pier?
2 km from the point on the shore nearest the first town
94
A man is driving a car at the rate of 30km/hour towards the foot of monument 6m high. A what rate is he approaching the top when he is 36m from the foot of the monument?
-29.59 km/hr
95
A cross-section of a trough is a semi-ellipse with width at the top 18 in. and depth 12 in. The trough is filled with water to a depth of 8 in. Find the width of the surface of the water.
6 square root of 5 in.
96
A point is chosen at random inside a circle having a diameter of 8 inches. What is the probability that the point is at least 1.5 in away from the center of the circle?
55/64
97
Find the equation of the line passing 3 units from the origin and parallel to 3x + 4y - 10 = 0
3x + 4y - 15 = 0
98
Determine the differential equation of the family of lines passing through (h, k)
(y - k) dx - (x - h) dy = 0
DC CIRCUITS POWERLINE
DC CIRCUITS POWERLINE
premopremo remo · 75問 · 2年前DC CIRCUITS POWERLINE
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80問 • 2年前AC CIRCUIT PASS REVIEWER
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80問 • 2年前AC MACHINES (ALTERNATOR) POWERLINE REVIEWER
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64問 • 2年前POLYPHASE POWERLINE REVIEWER
POLYPHASE POWERLINE REVIEWER
premopremo remo · 63問 · 2年前POLYPHASE POWERLINE REVIEWER
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premopremo remo · 59問 · 2年前AC CIRCUIT POWERLINE SUPPLY
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54問 • 2年前CIRCUIT TRANSIENT POWERLINE
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61問 • 2年前AC MOTORS SUPPLEMENTARY
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premopremo remo · 45問 · 2年前AC MOTORS SUPPLEMENTARY
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45問 • 2年前POWERSYSTEM SUPPLYMENTARY
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40問 • 2年前ALGEBRA
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42問 • 2年前ANALYTIC GEOMETRY
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premopremo remo · 23問 · 2年前TRIGONOMETRY
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23問 • 2年前HYDRAULICS/
HYDRAULICS/
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28問 • 1年前STRENGTH OF MATERIALS
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59問 • 1年前GENERAL CHEMISTRY AND MATERIAL SCIENCE
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47問 • 1年前PEC 2017
PEC 2017
premopremo remo · 62問 · 1年前PEC 2017
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62問 • 1年前ESAS 2 EVAL
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ESAS 3 EVAL
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ESAS 1 EVAL
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ESAS 1 EVAL
25問 • 1年前EE1 CIRCUITS
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93問 • 1年前MATH PRE BOARD POWERLINE
MATH PRE BOARD POWERLINE
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100問 • 1年前EE MODULE 1
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premopremo remo · 100問 · 1年前EE MODULE 1
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EE MODULE 2.2
premopremo remo · 74問 · 1年前EE MODULE 2.2
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MATH MODULE 2
premopremo remo · 100問 · 1年前MATH MODULE 2
MATH MODULE 2
100問 • 1年前MATH MODULE 2 101
MATH MODULE 2 101
premopremo remo · 100問 · 1年前MATH MODULE 2 101
MATH MODULE 2 101
100問 • 1年前MATH MODULE 2 102
MATH MODULE 2 102
premopremo remo · 54問 · 1年前MATH MODULE 2 102
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54問 • 1年前ESAS MODULE 1
ESAS MODULE 1
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ESAS MODULE 1
100問 • 1年前ESAS MODULE 4
ESAS MODULE 4
premopremo remo · 100問 · 1年前ESAS MODULE 4
ESAS MODULE 4
100問 • 1年前ESAS MODULE 4.2
ESAS MODULE 4.2
premopremo remo · 100問 · 1年前ESAS MODULE 4.2
ESAS MODULE 4.2
100問 • 1年前ESAS MODULE 4.3
ESAS MODULE 4.3
premopremo remo · 15問 · 1年前ESAS MODULE 4.3
ESAS MODULE 4.3
15問 • 1年前EE MODULE 3
EE MODULE 3
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EE MODULE 3
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EE MODULE 2
premopremo remo · 100問 · 1年前EE MODULE 2
EE MODULE 2
100問 • 1年前EE REFRESHER 4
EE REFRESHER 4
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EE REFRESHER 4
99問 • 1年前ESAS REFRESHER 4
ESAS REFRESHER 4
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ESAS REFRESHER 4
100問 • 1年前ESAS REFRESHER 3
ESAS REFRESHER 3
premopremo remo · 99問 · 1年前ESAS REFRESHER 3
ESAS REFRESHER 3
99問 • 1年前MATH FLASHING
MATH FLASHING
premopremo remo · 100問 · 1年前MATH FLASHING
MATH FLASHING
100問 • 1年前MATH FLASHING 1.2
MATH FLASHING 1.2
premopremo remo · 39問 · 1年前MATH FLASHING 1.2
MATH FLASHING 1.2
39問 • 1年前MATH MULTIVECTOR
MATH MULTIVECTOR
premopremo remo · 32問 · 1年前MATH MULTIVECTOR
MATH MULTIVECTOR
32問 • 1年前問題一覧
1
Determine the nature of the surface whose equation is 2 (x square) - 3 (y square) +( z square) 8x + 16y - 2z = 30
Hyperboloid
2
Find the polar moment of inertia of the area of a circle of radius 2 cm with respect to its center.
8 pi
3
How many kg. of cream containing 25 percent butter fat should be added to 50 kg of milk containing one percent butter fat to produce milk containing 2 percent butter fat?
2.174
4
The probability of getting at least two heads when a fair coin is tossed four times is
11/16
5
Find the angle in degrees between the vectors joining the origin to point P (1, 2, 3) and P( 2, - 3 , -1). Use space vector.
120
6
Determine the simplified form of sin 2B/ (1 - cos 2B)
cot B
7
Gravity causes a body to fall 16.1 feet in the 1 second, 48.3 ft in the 2rd second, 80.5 ft in the 3rd second, and so on. How far did the body fall during the 10th second?
305.9 ft
8
Determine the radius of the sphere whose equation is: x ^ 2 + y ^ 2 + z ^ 2 - 2x + 8y + 16z + 65 = 0
4 units
9
With a throw of 3 dice, what is the probability of getting a 9 or an 11?
52/216
10
The second derivative of the function f(x) is-f(x). What is a characteristic of this function
trigonometric
11
A water tank is shaped in such a way that the volume of water in the tank is V = 2y ^ 3 / 2 cu. in. when its depth is y inches. If water flows out through a hole at the bottom of the tank at the rate of 3 sq. rt. of y cu. in. / min, at what rate does the water level in the tank fall?
1 in/min
12
Solve (x + y) dy = (x - y) dx
x^2 - 2xy - y^2 = C
13
4 yards is how many inches
144
14
The equation {z ^2} = 4 represents which of the following curve?
Hyperbola
15
A steel girder 8m long is moved on rollers angle to the passageway 4m wide into a corridor at right angle to the passageway. Neglecting the width of the girder, how wide must the corridor be?
1.8 m
16
A railroad is to be laid-off in a circular path. What should be the radius if the track is to change direction by 30° at a distance of 157.08m?
300 m
17
The area enclosed by the ellipse 4x^2 + 9y^2 = 36 is revolved about the line x = 3 What is the volume generated
355.3
18
A ball is dropped from a height of 18m. On each rebound it rises 2/3 of the height from which it last fell. What is the distance has it traveled at the instant it strikes the ground for the 5th time?
75.78 m
19
A group consist of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n.
100
20
Two circles with different radius but with the same center are called _____ circles.
Concentric
21
From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Let the random variable x denote the number of children who do not recognize their mother's voice. Find the variance of x.
1.8
22
From past experience, it is known 90% of one-year old children can distinguish their mother's voice from the voice of a similar sounding female. A random sample of 20 one-year olds are given this voice recognition test. Find the probability that all 20 children recognize their mother's voice
0.122
23
Find the minimum distance from the point (4, 2) to the parabola y ^ 2 = 8x
2 sq. rt of 2
24
Find all values of z for e ^ n * (4z) = 1
πi/8 + kπi/2
25
One end of a 32m ladder resting on horizontal plane leans on a vertical wall. Assume the foot of the ladder to be pushed towards the wall at the rate of 2m/min. How fast is the top of the ladder rising rising when its foot is 10m from the wall?
0.658 m/min
26
Find the moment of inertia of the area bounded by the parabola y ^ 2 = 4x and the line x = 1, with respect to the x axis.
2.13
27
Find the length of the arc described by the parabola x ^ 2 = 4y from x = - 2 to x = 2
4.59
28
Two hundred single-sports athletes were cross-classified according to gender as follows:
Swimmer Runner Cyclist
Male 25 60 25
Female 20 50 20
What is the probability that the athlete is male or a swimmer or both?
0.550
29
Find the area enclosed in the second and third quadrants by the curve x = t^2 - 1 y= 5t^3 (t^2 -1)
8/7
30
The diameter of a circle is 10 cm and with its chord decreasing at the rate of 1cm/min. Determine the rate by which the arc subtended by the chord is changing when the chord is 8 cm long.
- 1.67 cm/min
31
Find the volume of the solid common between intersecting cylinders with radius of 3 ft.
144
32
A ranger in tower A saw a flash fire south of him while a ranger in tower B 20km east of tower A saw the flash fire with a bearing of 540° 15°W Find the distance of the flash fire from tower A.
23.62 km
33
A number is divided into two parts such that when the greater part is divided by the smaller, the quotient is 3 and the remainder is 5. Find the smaller number if the sum of the two numbers is 37
8
34
An audience of 450 persons is seated in a row having the same number of persons in each row. If 3 more persons seat in each row, it would require 5 rows less to sear the audience. How many rows were there originally?
30
35
Find the angle in mils subtended by a line 10 years long at a distance of 5000 yards.
2.04 mils
36
If 3x^2 is multiplied by the quantity 2x^3y raised to the 4th power, what would this expression simplify to?
48x^14y to the 4th power
37
Identify the curve r = a + b cos theta
Limacon
38
An open cylinder trough is constructed by bending a given sheet of tin and breadth 2a. Find the radius of the cylinder of which the trough forms a part when the capacity of the trough is a maximum.
0.637a
39
Solve the linear equation: d/dx (y) + y / x = x^2
xy = x^4/4 + C
40
Alex bought 400 hot dogs for the school pic. If they were contained in packages of 8 hot dogs, how many total packages did he buy?
50
41
A bus leaves Manila at 12 noon for Baguio 250 km away, travelling at an average of speed of 55 kph. At the same time, another bus leaves Baguio for Manila travelling at an average speed of 65 kph. At what time will they meet?
2:05 PM
42
A politician analyst asked a group of people how they felt about two political policy statements. Each person was to respond A (agree), N(neutral) and D(disagree) to each NN, ND, DA, AN, .... DD. Assuming each response combination is equally likely, what is the probability that the person being interviewed agrees with exactly one of the two political policy statements?
4/9
43
Bonnie has twice as many cousins as Robert. George has 5 cousins which is 11 less than Bonnie has. How many cousins does Robert have?
8
44
A tank initially holds 100 gal of salt solution in which 50 lbs. of salt has been dissolved. A pipe fills the tank with brine at the rate of 3gpm containing 2 lbs. of dissolve salt per gallon. Assuming that the mixture is kept uniform by stirring a drain pipe draws out of the tank the mixture of 2gpm. Find the amount of salt in the tank at the end of 30 minutes
171.24 lbs
45
It is one of the eight divisions of three-dimensional coordinates system.
Octants
46
Find the area of the largest rectangle that can be inscribe in an ellipse x ^ 2 + 4y ^ 2 = 4
4
47
How many positive real solutions are there in the polynomial: x ^ 4 - 4x ^ 3 + 7x ^ 2 - 6x - 18 = 0
3 or 1
48
A military supply truck contains 3 tons of food. If a soldier eats 12 ounces for breakfast, 18 ounces each for lunch and dinner, how many soldiers can be fed by the supply for 10 days?
200
49
If f(x) = 10^x + 1 then f(x + 1) - f(x) is equal to
9(10^x)
50
Four radars are tracking an asteroid. If the probability of tracking success is 90%, find the probability of at most 3 successes
0.3439
51
Find the equation of the circle that passes through the vertex and end points of the latus rectum of the parabola y ^ 2 = 8x
x ^ 2 + y ^ 2 = 10x
52
Evaluate the limit of z^2/(z^4 + z + 1) as z approached e^(π/4)i
sq.rt. of 2(1+i)/2
53
Find the volume of a cube having its two faces laid in the planes 2x - y + 2z - 3 = 0 and 6x - 3y 6z + 8 = 0 0 = angle E- angle+ angle A
4913/729
54
Compute log(3 - 2i)
0.5570 + 0.2554i
55
Water is running out a conical funnel at the rate of 1 cu. in./sec. If the radius of the base of the funnel is 4 in, and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in, from the top.
- 1/9π in/s
56
A steel ball is 12°C cools in 20 min to 80°C in a room 25°C Find the temperature of the ball after half an hour.
66.85°C
57
Find the unit vector which is orthogonal to 9i + 9i and 9i + 9k
(i - 1 - k)/sq.rt. of 3
58
A ball bounces 2/3 of the altitude from which it falls is dropped from a height of 18 ft., how far will it travel before coming to rest?
90 ft
59
The line passing through the focus and perpendicular to the directrix of parabola is called
axis
60
A hand soap manufacturer introduced a new liquid, lotion-enriched, antibacterial soap and conducted an extensive consumer survey to help judge the success of the new product. The survey showed 40% of the consumers had seen an advertisement for the new soup, 20% had tried the new soap, and 15% had both seen an advertisement and tried the new soap. If a randomly selected consumer has seen an advertisement for the new soap, what is the probability that this consumer has tried the new soap
37.5%
61
Find the volume generated by revolving the area bounded by y ^ 2 = 12x and x = 3 about the line x=3.
181
62
Solve the equation (x²y-2)+(x+2xy-5) i = 0.
x = 1, y = 2
63
Describe the locus represented by l z - i |=2
circle
64
Evaluate Integrate √(1 - cos x) dx
2√2 cos x + C
65
Find the equation of the bisector of the pair of acute angles formed by the line 4x + 2y = 9 and 2x - y = 8
8x - 25 = 0
66
Solve the particular solution of d/dx (y) - (3y)/x = x ^ 3 y(1) * d * 4
y = x^4 + 3x^3
67
Determine the equation of the line normal to the graph x^2 + 3xy + y^2 = 5 at the point (1, 1).
x - y = 0
68
Express decimally: Fifty-Eight millionth
0.000058
69
From a hill 600 ft. high, the angles of depression to the bases in opposite directions are 42" and 19 deg * 23' respectively. Find the length of the proposed tunnel through the bases.
2,371.74 ft.
70
Find the distance of the directrix from the center of an ellipse if its major axis is 10 and its minor axis is 8.
8.3
71
In the REE Board examinations, the probability that an examinee will pass in each subject is 0.75. What is the probability that an examinee wil pass at least two subjects?
0.84375
72
An ellipse with major axis 16 and minor axis 8 is revolved about its minor axis. Find the volume of the solid generated
1024 π/3
73
An airplane flies at a speed of 240 mph in still air S30°W with a wind speed of 40 mph due west. What is the new bearing?
S38°W
74
Bill, Bob, and Barry are hired to paint signs. In 8 hours, Bill can paint 1 sign, Bob can paint 2 signs, and Barry can paint 1 1/3 signs, They all come to work the first day, but Barry doesn't like the job and quits after 3 hours. Bob works half an hour longer than Barry and quits. How long will it take Bill to finish the two signs they were supposed to paint?
1 1/2 hrs
75
Hotels, like airlines, often overbook, counting on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservations will not be used if four reservations are made, what is the chance fewer than two will cancel
0.8192
76
Sand is being poured into a conical pile in such a way that the height is always 1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft. high if the height is increasing at 2 in/min.
130, 288.13 in/min
77
Evaluate: lim (2 - x) ^tan Dx/2
s^2/D
78
Liza thought she had the exact money to buy 10 chocolate bars. However, the price per bar had Increased by 50 centavos. Consequently, she was able to buy only 8 bars and had P2 left. How much money did Liza have
30
79
Find the maximum value of 3^sin 3x.
3
80
If the general equation of the conic is A * x ^ 2 + Bxy + C * y ^ 2 + Dx + Ey + F = 0 and B ^ 2 - 4AC > 0 then the conic is
hyperbola
81
Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486.
844
82
A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least P50. A random sample of 20 alumni is selected. What is the probability that less than 17 alumni will make a contribution of at least P50
0.589
83
Find the equation of the normal line to x ^ 2 + y ^ 2 = 1 at the point (2, 1).
x = 2y
84
Jun rows his banca across a river at 4 km/hr. How lorig will it take Jun to cross the river?
3.78 min
85
The difference between six times the quantity 6x + 1 and three times the quantity x - 1 is 108. What is the value of x?
3
86
Michael walks to school. He leaves each morning at 7:32 A.M. and arrives at school 15 minutes later. If he travels at a steady rate of 4.5miles/hour. What is the distance between his home and school?
1.1
87
The time a student spends learning a computer software package is normally distributed with a mean of 8 hours and standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends less than 6 hours learning a software package?
0.09
88
What is the smallest positive value for x where y = sin 2x reaches its maximum
D/4
89
Find the vertex of the parabola x ^ 2 = 4y
(0,0)
90
When the energy/hour required in driving a boat varies as the cube of the velocity, find the most economical rate /hour when going against a current of 4kph.
6 kph
91
After paying a commission of 7% of the sale price to his broker, Tess receives P 103,000 for his car. How much was the car sold?
P110,753
92
Find an equation of the parabola with vertex (-1,-2) latus 12, opens downward.
x ^ 2 + 2x + 12y + 25 = 0
93
The towns are located near the straight shore of the lake. Their nearest distances to the point in the shore are 1km and 2 km respectively, and these points on the shore are 6 km apart. Where the fishing port should be located to maximize the total amount of paving necessary to build a straight road from each town to the pier?
2 km from the point on the shore nearest the first town
94
A man is driving a car at the rate of 30km/hour towards the foot of monument 6m high. A what rate is he approaching the top when he is 36m from the foot of the monument?
-29.59 km/hr
95
A cross-section of a trough is a semi-ellipse with width at the top 18 in. and depth 12 in. The trough is filled with water to a depth of 8 in. Find the width of the surface of the water.
6 square root of 5 in.
96
A point is chosen at random inside a circle having a diameter of 8 inches. What is the probability that the point is at least 1.5 in away from the center of the circle?
55/64
97
Find the equation of the line passing 3 units from the origin and parallel to 3x + 4y - 10 = 0
3x + 4y - 15 = 0
98
Determine the differential equation of the family of lines passing through (h, k)
(y - k) dx - (x - h) dy = 0