MATH DOCS Flashcards
Three sides of a trapezoid are each 8 cm long. How long is the 4th side, when the area of the trapezoid has the greatest value?
- A. 16 cm
Sand is pouring to form a conical pile such that its radius is always twice the height, if the volume of a conical pile is increasing at a rate of 2 cu. m/s. How fast if the height is increasing when the height is 4m?
C. ⅛ π – ⅛ pi m/s
Find the radius of curvature of y = x^3 at the point (1,1).
- C. 5.27
1A rectangular field is fenced off, an existing wall being used as one side. If the area of the field is 7,200 sq. ft, find the least amount of fencing needed.
- C. 240 ft
If z = xy^2, and x changes from 1 to 1.01, and y changes from 2 to 1.98, find the approximate change in z.
- A. -0.0404
Find y’ if y-acrsin(cosx)
- A. -1
Evaluate Л tan(theta) In sec(theta) d(theta)
- D. ½ ln(secθ)^2 + C
Find the curve surface area of the solid generated by revolving the part of the curve y = x2 from (0,0) to (√6,6) about the y-axis.
B. 62π/5 sq. units
Find the volume of the solid generated by revolving the area of the circle x^2+y^2=36 on the second quadrant about the line y + 10=0
- D. 2229
What is the area (in square units) bounded by the curve y^2=x and the line x-4=0?
- C. 32/3
What is the area within the curve r2 = 16 cos 0?
- D. 32
Find the area bounded by the y-axis and x = 4-y^2/3
- A. 25.6
Evaluate ∫1,0 ∫y^2, y ∫lnx,0 ye^z dzdxdy
- C. 1/24
A solid is formed by revolving about the y-axis, the area bounded by the curve x^3=y, the y-axis and the line x=8 Find Its Centroid
- A. (0, 4.75)
Determine the moment of inertia of the area bounded by the curve x2 = 4y, the line x-4=0 and the x-axis with respect to the y-axis
- A. 51.2
The rate of population growth of a country is proportional to the number of inhabitants. If a population of a country now is 40 million and expected to double in 25 years, in how many years is the population be 3 times the present?
- A. 39.62 years
A thermometer reading 18 °C is brought into a room where the temperature is 70 °C; 1 minute later the thermometer reading is 31 c. 18.64yrs °C. Determine the thermometer reading 5 minutes after it is brought into the room.
- D. 57.66 °C
Water at 100°C cools in 5 minutes to 70°C in a room at 20°C. What will be the temperature of the water at the end of another 5 minutes?
- B. 51.25°C
A thermometer which has been at the reading of 70°F inside a house is placed outside where the air temperature is 10°F. Three minutes later it is found that the thermometer reading is 25°F. Find the thermometer reading after 6 minutes.
- C. 13.75 °F
In a tank are 100 liters of brine containing 50 kg total of dissolved salt. Pure water is allowed to run into the tank at the rate of 3 d. 11.75 °F liters a minute. Brine runs out of the tank at the rate of 2 liters a minute. The instantaneous concentration in the tank is kept uniform by stirring. How much salt is in the tank at the end of one hour?
- B. 19.53 kg
Evaluate the value of tanh(jpi/3)
- C. j 1.732
Find a0 for the equivalent Fourier series of x^2 over the interval -pi to pi
C. π ^2/3
Find the interval of convergence (-1)^n n/ 4^n (x+3)^n
- A. -7<x<1
Find the laplace transform of t^3/2
- D. (3√π) /(4^s5/2) / sqrt of π/4s^5/2
Evaluate In(2+3)
D. 1.28 + 0.98j
A coin is tossed 3 times. What is the probability of getting 3 tails up?
- A. 1/8
In how many ways can 5 people be lined up to get on a bus, if a certain 2 persons refuses to follow each other?
- A. 72
In a commercial survey involving 1000 persons, 120 were found to prefer brand x only, 200 prefer brand y only, 150 prefer brand z only, 370 prefer either brand x or brand y but not z, 450 prefer brand y or z but not x and 370 prefer either brand z or y but not y. How many persons have no brand reference, satisfied with any of the three brands?
- B. 230
The probability for the ECE board examinees from a certain school to pass the subject Mathematics is 3/7 and for the subject c. 188,848,296 d. 31,474,716 Communications is 5/7. If none of the examinees fails both subject and there are 4 examinees that passed both subjects, find the number of examinees from that school who took the examinations.
- D. 28
The probability of A’s winning a game of chess against games B is ⅓ What is the probability that A will win at least 1 of a total of 3
- A. 19/27
What is the probability of drawing 2 cards, both are spade in a standard deck of 52 cards?
- A. 3/52
One bag contains 4 white balls and 3 black balls and a second bag contains 3 white balls and 5 black balls. One ball is drawn at random from the second bag and displaced unseen in the first bag. What is the probability that a ball now dawn from the first bag is white?
- A. 35/64
In a poker hand consisting 5 cards, find the probability of holding 4 hearts and 1 club.
- C. 143/39984
Three balls are drawn from a bag containing 5 white balls and 4 red balls. What is the probability that the balls drawn are all white?
- B. 5/42
Find the area under the standard normal curve between z=-0.46 and z-2.21
- D. 0.6637
Compute algebraically the resultant of the coplanar forces: 100 N at 30°, 141N at 45°, and 100 N at 240°.
- B. 0.15 kn at 25°
A force 151-16j+27k N is added to a force 23j-40k. What is the magnitude of the resultant?
- A. 21N
At cartesian point (-3,4,-1), which of these is incorrect?
- A. P = -5
Evaluate the integral of xe^(-3x) from 1 to infinity
- A. 4/9 e^-3
Find the area (in sq. units) bounded by the parabolas
- B. 10.7
Find the length of the arc of x^2=64 from x = -1 to x=-3, in the second quadrant.
- D. 2.07
The area bound by the curves y = x^2 and y = x^1/2 in the first quadrant is rotated about the x-axis. Find the volume of the solid formed.
- C. 3/10
Find the limit of (x-4)/(x^2-x-12) as x approaches 4
A. 1/7
FIND THE SLOPE OF (X^2)Y=8 AT THE POINT (2,2)
B. -2
An open top rectangular tank with square bases is to have a volume of 10 cu. m. The materials for its bottom are to cost PI5 per square meter and that for the sides, P6 per square meter, Find the most economical dimensions for the tank.
- C. 2m x 2m x 2.5m
A man walks across a bridge at the rate of 5 ps as a boat passes directly beneath him at 10 fps. If the bridge is 10 fect above the boat, how fast are the man and the boat separating I second later?
- C. 8:33 FPS
Water is flowing into a conical cistern at the rate of 8m^3/min. If the height of the inverted cone is 12 m and the radius of its circular opening is 6m. How fast is the water level rising when the water is 4 m deep?
A. 0.64 m/min
A helicopter is rising vertically from the ground at a constant rate of 4.5 meters per second. When it is 75 m off the ground, a jeep passed beneath the helicopter traveling in a straight line at a constant rate of 80 kph. Determine how fast the distance between them changing after 1 second.
A. 10.32 m/s
A Norman window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the width of the rectangle to the total height so that it will yield a window admitting the most light for a given perimeter?
A. 1
At any distance from the source of light, the intensity of illumination varies directly as the intensity of the source and inversely as the square of x. Suppose that there is a light at A, and another at B, the one at B having an intensity 8 times that of A. The distance AB is 4 m. At what point from A on the line AB will the intensity of illumination be least?
B. 1.50 m
A pole 24 feet long is carried horizontally along a corridor 8 feet wide and into a second corridor at right angles to the first. How wide must the second corridor be?
A. 8.98 ft
Determine order and degree (if defined) of differential equation (y’)^2+ (Y”)^3 + (Y)^4 + y^5 - 0.
D. Order = 3, degree = 2
Which of the following is an integrating factor that would yield an exact solution for the equation: 2xy dx + y^2 dy =0
- B. 1/y
The area enclosed by the ellipse ×2/9 + y2/4 = 1 is revolved about the line ×=3. What is the volume generated?
A. 355.3
Compute the area of the region bound above by y = sin(x), below by y = x - r, and to the left by x = 0.
- B. π^2/2+2
Find the volume generated by rotating the region bounded by y = x, × = 1, and y^2 = 4x, about the x-axis.
- B. 2 π
Find the integral of I/(xInx) dx
- C. ln | ln x| + c
How much work is required to pump all the water from a right circular cylindrical tank, that is 8 feet in diameter and 9 feet tall, if it is emptied at a point 1 foot above the top of the tank?
A. 49.421 π ft .lb
A trapezoidal gutter is to be made, from a strip of metal 22 inches wide by bending up the edges. If the base is 14 inches wide, what width across the top gives the greatest carrying capacity?
A. 16 in
