B^2 - 4AC < 0 describes a/an

A fencing is limited to 20 ft. length. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall?

z varies directly as x and inversely as y2. If x = 1 and y = 2 then z = 2. Find z when x = 3 and y = 4.

The square of a number added to 25 equals 10 times the number. What is the number?

The equation y^2 = cx is the general solution of

Describe the locus represented by |z + 2i| + |z – 2i| = 6.

Find the value of sin (arc cos 15/17)

Find all the real solutions to the logarithmic equation ln x + ln 2 = 3.

A line segment is a side of a square and also the hypotenuse of an isosceles right triangle. What is the ratio of the area of the square to the area of the triangle?

Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards.

Which ratio best express the following: five hours is what percent of a day?

Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years?

Determine the equation of the line passing through the points (1, 17) and (13, 4).

A car consumes 16 gallons of gasoline to travel 448 miles. How many miles/gallon is the car’s consumption?

Find the area of the region bounded by y^2 = 8x and y = 2x.

What is the area (in square units) bounded by the curve y^2 = 4x and x^2 = 4y?

Suppose two radar stations located 20 miles apart each detect an aircraft between them. The angle of elevation measured by the first station is 35 degrees, whereas the angle of elevation measured by the second station is 15 degrees. Determine the height of the airplane.

A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 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 ?

Find all values of z for which e4z = i. 

Each of the question on a quiz is a five-part multiple choice question with exactly one correct answer. A student, totally unprepared for the quiz, guesses on each of 15 questions. If at least 11 questions must be answered correctly to pass the quiz, what is the chance the student passes?

What is the graph of the curve whose equation is 5x2 + 5y2 – 5x – 10y – 33 = 0.

When a metallic ball bearing is placed inside a cylindrical container of radius 2 cm, the height of the water inside the container increases by 0.6 cm. What is the radius of the ball bearing ?

A student did not study for his upcoming examination on which is 15 multiple choice test questions, with five possible choices of which only one is correct, what is the expected number of correct answers he can get?

During his major league career, Hank Aaron hit 38 more home runs than Babe Ruth hit during his career. Together they hit 1,524 home runs. How many home runs did Babe Ruth hit?

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis?

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?

42% of 997 =

From a stationary point directly in front of the center of the bull’s eye, Kim aims two arrows at the bull’s eye. The first arrow nicks one point on the edge of the bull’s eye; the second strikes the center of the bull’s eye. Kim knows the second arrow traveled 20 meters since she knows how far she is from the target. If the bull’s eye is 4 meters wide, how far did the first arrow travel? Assume the arrows travelled in straight-line paths and the bull’s eye is circular.

A conic section whose eccentricity is equal to one (1) is known as:

Hotels, like airlines, often overbook, relying on the fact that some people with reservations will cancel at the last minute. A certain hotel chain finds 20% of the reservation will not be used. If 4 reservations are made, what is the probability fewer than two will cancel?

If a rock is dropped, its distance below the starting point at the end of t sec is given by s = 16 t square, where s is in ft. Find the rate of change of distance after 1.5 minutes.

Susan starts working at 4:00 and Dy starts at 5:00. They finished at the same time. If Susan worked x hours, how many hours did Dy worked?

Find the general solution of y’ = y sec x

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 equation of the normal line to x2 + y2 at the point (2, 1).

Evaluate cos(arc sin 2/3 – arc sin (−1/3)).

During an examination, the following scores are collected: 0   8   9   11   12   13   18   18   20 If there was an error in encoding where one “18” should be “16”, which of the following is affected?

If y = cos x, what is dy/dx?

Find the vertex of the parabola x^2 = 8y.

Matthew had 200 baseball cards. He sold 5% of the cards on Saturday and 10% of the remaining cards on Sunday. How many cards are left?

Find the area of the region enclosed by the triangle with vertices (1, 1), (3, 2) and (2, 4).

The plane rectangular coordinate system is divided into eight parts which are known as 

Find the equation of the circle tangent to 4x – 3y + 12 = 0 at (−3, 0) and tangent also to 3x + 4y – 16 = 0 at (4, 1).

What curve is described by the equation y^2 + 4y + x – 1 = 0?

Which of the following is a disadvantage of using the sample range to measures of spread or dispersion?

Give one indicated root of (2 square root of 3 – 2i)^1/2.

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?

A pebble dropped into a lake creates an expanding circular ripple. If the radius of the ripple is increasing at the rate of 2 in/sec, at what rate is its area increasing  when its radius is 10 in.?

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. Drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is equally likely, and one student is known to have a negative result. What is the probability that all three students get a negative result?

Carbon is a radioactive form of carbon that is found in all living plants and animals. After a plant and animal dies, the carbon 14 disintegrates. Scientists determine the age of the remains by comparing its carbon 14 with the amount found in living plants and animals and follows exponential growth pattern. Charcoal from an ancient fire pit Java had 1/4 the amount of carbon 14 found in a living sample of wood with the same size. Estimate the age of the charcoal.

A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.02 in with tolerance of 0.004 in. Solve the inequality involving absolute values that describes the range of possible thickness for the laminate.

The equation of a limacon is

Evaluate  ∫ sqrt of (1 - cos x)

Find the value of x for which f(x) = x^2 + 5x + 2 is maximum.

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. Let the random variable x denote the number of children who do not recognize their Mother’s voice. Find the mean of x.

Peter can finish in 2 hours while John can finish in 1.5 hours. How long will it take if they work together?

Approximately how many liters of water will a 10-gallon container hold?

Evaluate ∫(sin 5x + cos 3x) dx from x = 0 to x = π/2.

Find the point on the line 3x + y + 4 = 0 that is equidistant from the points (-5, 6) and (3, 2).

In a pile of logs, each layer contains one more log than the layer above and the top contains just one log if there are 105 logs in the pile, how many layers are there?

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.

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

A steel girder 8 m long is moved on rollers along a walkway 4 m wide and into a corridor perpendicular to the walkway. How wide must the corridor be to successfully move the girder?

Determine the correct equation for the line with a slope of 7 and y-intercept of -4.

Compute log (3-2i)*

Larry finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower?

Find the maximum area of a rectangle which can be inscribed in an ellipse having the equation x^2 + 4y^2 = 4.

The tangent of an angle of a right triangle is 0.75. What is the cosecant of the angle ?

Find the domain of the following function: f(x) = 3x, −6 ≤ x ≤ 8.

If 3x2 is multiplied by the quantity 2x^3y raised to the 4th power, what would this expression simplify to?

A triangular corner lot has perpendicular sides of lengths 90 m and 60 m. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides parallel to the streets.

What conic section is described by the equation 4x2 – y2 + 8x + 4y = 15?

Parcel charges of a courier company are follows: P40 for the first 2 kilograms, P15 for each of the succeeding kilogram weight of parcels. With these rates, what amount would be charged on a parcel weighing 30 kg?

A car rental company offers two plans for renting a car : Plan A : $ 30 / day and $ 0.20 /mile ; Plan B : $ 55 / day with free unlimited mileage. For what range of miles will Plan B save a customer’s money?

Find an equation of the parabola with vertex t (-1, -2) latus rectum 12, opens downward

Find the value of ((sin θ + cos θ tan θ))/cos θ

What is the equation of a line that passes through (-3,5) and is parallel to the line 4x – 2y + 2 = 0?

What curve is described by the equation 4x^2 – y^2 + 8x + 4y = 15?

Solve the equation ( x^2 y – 2 ) + ( x + 2xy – 5 ) i = 0.

Judy’s English quiz scores are 56, 93, 72, 89 and 87. What is the median of her squares?

Find ∫ (3x – 4)^3 dx.

Evaluate    lim     ( 1 + 2x )^( 1 + 2x ) / x

Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486.

Find the area under one arch of the hypocycloid 𝑥 = 𝑎(𝛳 − 𝑠𝑖𝑛𝛳), 𝑦 = 𝑎(1 − 𝑐𝑜𝑠𝛳)   

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.

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

A point where the concavity of a curve changes or when the slope of the curve is neither increasing nor decreasing is known as

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

Evaluate the double integral dx dy / (x – y), with interior limits 2y to 3y and outer limits from 0 to 2.

The area in the second quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated?

A conic section whose eccentricity is equal to one (1) is known as:

Find the volume generated when the area bounded by the curve y = cosh x and the x-axis from x  = 0 to x = 1 is revolved about the x-axis.

A group consists 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.

Find the equation of the line when slope is −3 and x-intercept is 5.

A square has a side 5 cm shorter than the side of a second square. The area of the larger square is four times the area of the smaller square. Find the side of each square.

A cone shaped icicle is dripping from the roof. The radius of the icicle is decreasing at a rate of 0.2 cm/hr, while the length is increasing at a rate of 0.8cm/hr. If the icicle is currently 4 cm in radius and 20 cm long, is the volume of the icicle increasing or decreasing, and at what rate?

A container is in the form of a right circular cylinder with an altitude of 6 in and a radius of 2 in. If an asbestos of 1 in thick is inserted inside the container along its lateral surface, find the volume capacity of the container.

A pendulum 1 m long oscillates through an angle of 100. Find the distance through which the end of the pendulum swings in going from one extreme position to the other.

The product of the slopes of any two straight lines is negative 1, one of the lines are said to be

Solve for z: 5z^2 + 2z + 10 = 0

A man is driving a car at the rate of 30 km/hour towards the foot of monument 6 m high. At what rate is he approaching the top when he is 36 m from the foot of the monument?

Find the general solution of y” + 10y’ + 41y = 0.

A transmitter with a height of 15 m is located on top of a mountain, which is 3.0 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.

Solve the differential equation 7yy’ = 5x.

The curve which has an eccentricity equals to zero

Find two numbers whose sum is 50 and with largest possible product.

Oscar sold 2 glasses of milk for every 5 sodas he sold. If he sold 10 glasses of milk, how many sodas did he sell?

Find the height of a tree if the angle of elevation of its top changes from 20° to 40° as the observer advances 23 meters toward the base.

Find the sum of all odd integers between 100 and 1000.

Find the sum of a geometric progression if there are 4 geometric means between 3 and 729.

A normal to a given plane is

In an arithmetic series, the terms of the series are equally spread out. For example, in 1 + 5 + 9 + 13 + 17, consecutive terms are 4 apart. If the first term in an arithmetic series is 3, the last term is 136, and the sum is 1,390, what are the first 3 terms?

Find the radius of curvature of the curve y^2 = 4x at P(4, 4).

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?

Find the volume (in cubic units) generated by rotating a circle x^2 + y^2 + 6x + 4y + 12 = 0 about the y-axis.

If the average value of a periodic function over one period is zero, and it consists of only odd harmonics, then it must be possessing ____ symmetry.

Determine the equation that expresses the statement: F is directly proportional to y. Symbols a, b, c and d are constants.

A line that is perpendicular to the y-axis has a slope equal to .

Water is running out of a conical funnel at a 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.

At exactly what time after 5 o’clock will the hour hand and the minute hand be perpendicular for the first time?

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 at least one student gets a negative result?

If the general equation of the conic is Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0. If B^2 – 4AC > 0, the equation describes a 

Find the area bounded by y" = 4x and x" = 4y. of the square in simplified form?

If csc^2 θ = x^2 + 1, what is cot^2 θ?

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?

If 10^x = 4, find the value of 10^2x + 1.

In an ellipse a chord which contains a focus and is in a line perpendicular to the major axis is a:

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?

A laboratory keeps two acid solutions on hand. One is 20% acid and the other is 35% acid. How many liters of distilled water should be added to a liter of 35% acid solution in order to dilute it to a 20% acid solution?

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.

At the city park, 32% of the trees are oaks, if there are 400 trees in the park, how many trees are NOT oak?

Find the length of arc of the parabola x^2 = 4y from x = −2 to x = 2.

The axis of the hyperbola through its foci is known as:

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

A statue 3 m high is standing on a base of 4 m 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?

Find the radius of curvature at any point in the curve y + ln cos x = 0.

What is the area bounded by the curve y = 0, y = 3x^2, x = 0, and x = 2?

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 probability that at least 3 children did not recognize their mother’s voice.

A secondary school is contracting its alumni asking for donations to help put up new computer laboratory. Past records show that 80% of the alumni will make a contribution of at least P50.00. A random sample of 20 alumni is selected. What is the probability that exactly 15 alumni will make a donation of at least P50.00?

The centroid of the area bounded by the parabola y2 = 4ax and the line x = p coincides with the focus of the parabola. Find the value of p.

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

The locus of a point which moves so that the sum of its distances between two fixed points is constant is called

What curve is described by the equation 4x^2 – y^2 + 8x + 4y = 15?

The mean computer usage of a person is 8 hours with a standard deviation equal to 1.5 hours. Assume that the computer usage is approximately normally distributed. What is the probability that a person will use the computer for at least 8.5 hours?

Find the area bounded by the parabolas x2 – 2x + 2y + 5 = 0 and x2 – 2x + y + 1 = 0.

Four is added to the quantity two minus the sum of negative seven and six.This answer is then multiplied by three. What is the result?

Describe the locus represented by | z – i | = 2.