A man on an observation s ees a fire directly south of him. A boy on another tower 20 km east of the first tower observes the fire at a bearing S40o15’W. What is the distance of the first tower from the fire?

Two engineers facing each other with a distance of 5km from each other, the angles of elevation of the balloon from the two engineers are 56 degrees and 58 deg.

Find the differential equation of the family of lines passing through the origin.

What is the angle subtended in mils of an arc length of 10 yards in a circle of radius 5,000 yards?

The area in the second quadrant of the circle x^2 + y^2 = 36 i s r evo l v ed about the line y + 10 = 0. What is th e volume g e n e r ate d ?

What percentage of the volume of a cone is the maximum volume right cylinder that can be inscribed in?

A company owns a right triangular lot. The perpendicular sides are 90m and 60m. The company wants to construct a warehouse with a rectangular base of maximum area and with sides are parallel to the perpendicular sides of the lot. Find the dimensions of the base of the warehouse.

In polar coordinate system the distance from a point to the pole is known as:

Find the area of the polygon with vertices at 2 + 3i, 3 + i, -2 - 4i, -4 – i, -1 + 2i.

Michael's favorite cake recipe calls for 0.75 pounds of flour; he has a 5 pound bag. He wants to make several cakes for the school bake sale. How many cakes can he make?

Find the radius of curvature of the parabola y2 = 4x at point P (4,4)?

Bert cuts a piece of rope into three pieces. One piece is 8 inches long, one piece is 7 inches long, and one piece is 5 innches long. The shortest piece of rope is approximately what percent of the original length before the rope was cut?

A cylindrical can is to have volume 1000 cubic centimeters. Determine the height which will minimize the amount of material to be used.

From the past experience, it is known 90% of one-year-old children can distinguish their mother 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 mean of x.

Marvin helps his teachers plan a field trip. There are 125 persons to the field trip and each school bus holds 48 persons. What is the minimum number of school buses is needed to reserve for the trip?

What is the area bounded by the parabola x² = 8y and its latus rectum?

The axis of the hyperbola which is parallel to its directrices is known as ______.

A cylindrical can

Find the equation of the family of the family of orthogonal trajectories of the system of parabolas y^2 = 2x + C.

From past experience, it is known 90 percent of one year old children can distinguish their mother's voice of a similar sounding female. A random sample of one year's old are given this voice recognize test. Find the standard deviation that all 20 children recognize their mother's voice.

The ceiling in a hallway 10 m wide is in the shape of a semiellipse and is 9 m high in the center and 6m high at the side walls. Find the height of the ceiling 2 m from either wall.

A cylindrical container open at the top with minimum surface area at a given volume. What is the relationship of its radius to height?

If z = 6 e ^(j pi/3), evaluate |e^(jz)|.

When a baby was born he weighs 8 lbs and 12 oz. After two weeks during his check-up he gains 8 oz. What is his weight now in lbs and oz?

Solve (x + y) dy = (x – y) dx

Find the volume generated by revolving the circle x^2 + y^2 + 6x + 4y + 12 = 0 about the y-axis

A group consists of N engineers and N nurses. If two of the engineers are replaced by two other nurses, 51% of the group members are nurses. Find the value of N.

A sinking ship makes a distance signal seen by three observers all 20 m inland from the shore. First observer is perpendicular to the ship, second observer 100 m to the right of the first observer and the third observer is 125 m to the right of the first observer. How far is the ship from the shore?

Susan starts work at 4:00 and Dee starts at 5:00. They both finish at the same time. If Susan works x hours, how many hours does Dee work?

If tan A = 1/3 and cot B = 4 find tan (A + B)

Two stones are 1 mile apart and are at the same level as the foot of a hill. The angles of depression of the two stones viewed from the top of the hill are 5 degrees and 15 degrees respectively. Find the height of the hill.

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.

An epidemic spread at a rate jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of 5000 inhabi t a n ts , 1 6 0 p e o p l e h av e t h e d i s e a s e at th e beginning of the week and 12 0

Evaluate (1+i) raised to the power of (1-i).

Find the equation of the family of curves at every point of which the tangent line has a slope of 2y.

Which of the following differential equations describes a family of circles centered at the y-axis?

From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice 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 probability that all 20 children recognize their mother’s voice.

Solve the equation y’ = y/2x.

Jenny flipped a coin three times and got heads each time. What is the probability that she gets heads on the fourth flip?

Find the area of the ellipse 4x^2 + 9y^2 = 36?

A ball is dropped from a height of 18m. On each rebound it rises 2/3 of the height form which it last fell. What distance has it traveled at the instant it strikes the ground for the 5th time?

If in the Fourier series of a periodic function, the coefficient a0 = 0 and an = 0, then it must be having ___________ symmetry.

A post office can accept for mailing only if the sum of its length and its girth (the circumference of its cross section) is at most 100 in. What is the maximum volume of a rectangular box with square cross section that can be mailed?

Manuelita had 75 stuffed animals. Her grandmother gave fifteen of them to her. What percentage of the stuffed animal s did her mother give her?

The area enclosed by the ellipse 4x^2 + 9y^2= 36 is revolved about the line x = 3, what is the volume generated?

Find |u x v| correct to three decimal places where |u| = 9, |v| = 3, θ = 85 deg. Select the correct answer.

From the base of a building, the angle of elevation to the top of a 4.0 m vertical pole a distance away is 18 deg. 50 min. from the top of the building, the angle of depression of the base of the pole is 48 deg. 10 min. Find the height of the building.

If the average person throws away 38.6 pounds of trash every day, how much trash would the average person throw away in one week?

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?

From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice 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.

A steel girder 8 m long i

Three circles of radii 3, 4, and 5 inches, respectively are tangent to each other externally. Find the largest angle of a triangle formed by joining the centers.

In delivery of 14 transformers, 4 of which are defective, how many ways that in 5 transformers at least 2 are defective?

Three randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the three student’s drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assume the possible combination is equally likely and knowing that 1 student gets a negative result, what is the probability that all 3 students get a negative result?

The length of the latus rectum of the parabola y^2 = 4px is:

An air balloon flying vertically upward at constant speed is situated 150 m horizontally from an observer. After one minute, it is found that the angle of elevation from the observer is 28 deg 59 min. What will be then the angle of elevation after 3 minutes from its initial position?

Evaluate the integral of square root of (1 - cos x) dx

Given an 8cm square. If the second square is made by c

From past experience, it is known 90% of one year old children can distinguish their mother voice from the voice 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 probability that at least three children do not recognize their mother’s voice.

Find the minimum distance from the point P (4,2) to the parabola y^2 = 8x.

The cable of suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally. The distance between towers is 150 m, the points of the cable on the towers are 22 m above the roadway, and the lowest point on the cabl e is 7 m above the roadway. Find the vertical distance to the cable from a point in the roadway 15 m from the foot of a tower.

If the coefficient a0 of a Fourier series of a periodic function of zero, it means that the function has

Joseph gave 1/4 of his candies to Joy and Joy gave 1/5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have originally?

Determine the differential equation of the family of lines passing through (h, k)

Jonas is 5ft 11 in tall and Pedro is 6ft 5 in tall. How much taller is Pedro than Jonas?

A transmitter with a height of 15 m is located on the top of a mountain which is 3 km high. What is the farthest distance on the surface of the earth that can be seen from the top of the mountain? Take the radius of the earth to be 6400 km.

A statue 3 m high is standing on a base of 4m high. If an observer’s eye is 1.5 m above the ground how far should he stand from the base in order that the angle subtended by the statue is a maximum?

A statistic 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 P50.00. A random sample of 20 alumni is selected. What is the probability that more than 15 alumni will make a contribution of at least P50.00?

Melissa is 4 times as old as Jim. Pat is 5 years older than Melissa. If Jim is y, how old is Pat?

Compute log (3 – 2i)

A 20-ft lamp casts a 25 ft shadow. At the same time, a nearby building casts a 50 ft shadow. How tall is the building?

Carmela and Marian got summer jobs at the ice cream shop and were supposed to work 15 hours per week each for 8 weeks. During that tim e, Marian was i l l f o r o n e w e e k a n d C a r m e l a to ok her s h i fts . How many hours di d C ar m e la w o rk d u r i n g th e 8 w ee ks?

What is the value of x in arctan(2x) + arctan(x) = pi/4?

A periodic function has zero average value over a cycle and its Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function?

Joy is 10% taller than Joseph and Joseph is 10% taller than Tom. How many percent is Joy taller than Tom?

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?

Donations were made by alumni for a school to fund a new computer room. Data shows that 80% of the alumni give at least P 50. If the administration contacts 20 alumni, what is the probability that less than 17 of them will give at least P50?

Three randomly chosen senior high school students was administered a drug test. Each student was evaluated as positive to the drug test (P) or negative to the drug test (N). Assume the possible combinations of the three students’ drug test evaluation as PPP, PPN, PNP. NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, what is the probability that all three students get positive results?

Water is running out of a conical funnel at the rate of 1 cu. in / se c . I f t h e r ad iu s o f t h e b a s e o f t h e f u n n e l i s 4 i n a n d t h e alt i tu d e i s 8 in , fi nd t h e r a t e a t wh i c h t h e w a t e r l e v e l i s d r o p p i ng when it is 2 in from the top.

A stone is thrown into still water and causes concentric circular ripples. The radius of the ripples increases at the rate of 12 in/s. At what rate does the area of the ripple increases in sq. in/s when its radius is 3 inches?

Melinda and Joaquin can restock and aisle at the supermarket in one hour working together. Melinda can restock an aisle in 1.5 hours working alone, and it takes Joaquin two hours to restock an aisle. If they work together for two hours, and then work separately for another two hours, how many aisles will they have completed?

The locus of a point which moves so that its distance from a fixed point and a fixed line is always equal is _______.

Joey will be x years old y years from now. How old is she now?