If y = arctan (ln x), find y' at x = 1/e.

Find the area bounded by the parabola x? +2x + 2y + 5 = 0 and x? -x + y + 1= 0.

Locus of a point difference of its distance to the fixed point is constant.

Find the equation x = y = z that is equidistant from (3,0,5) and (1,-1,4)

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

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 equation cos2A = 1 - cos2A

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

Find the sum of all odd integers between 100 and 1,000.

Solve for x and y in ln xy + 8 + j (x2y + y) = 4x + 4 + j (xy2 + x)

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

The cost per hour of running a boat is proportional to the cube of the speed of the boat. At what speed will the boat run against a current 8 kph in order to go a given distance most economically?

When two lines are perpendicular, the slope of one is

A line segment is a size 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?

Identify the curve described by | z - 3i | - | z + 3i | = 4

The distance from the sun to the earth is approximately 9.3 x 10^7 miles. What is the distance expressed in standard notation?

The coefficient ao of a Fourier series of a periodic function is zero, it means that the function has

A tangent to a conic is a line

It is a sequence of numbers such that successive terms differ by a constant.

Find the domain of the function f(x) = 3x, -6≤x≤8?

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

Determine the equation that expresses that G is proportional to k and inversely proportional to C and z. Symbols a, b and c are constants.

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

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 inhabitants, 160 people have the disease at the beginning of the week and 1200 have it at the end of the week. How many days does it take for 80% of the population to become infected?

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

Obtain L^1 {1/ (s^2 + 1)^2}

A cardboard 20 in x 20 in is to be formed into a box cutting four equal squares and folding the edges. Find the volume of the largest box.

Find the volume generated when y = 2x + 3 and y = x² is revolved about the x-axis.

Three machines X, Y, and Z produce respectively 50%, 30% and 20% of the total number of items of a factory. The percentages of defective output of these machines are respectively 3%, 4%, and 5%. If an item is selected at random, what is the probability that the item is defective?

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)

A cone shaped icircle is dripping from the roof. The radius of the icircle is decreasing at a rate of 0.2 cm/hr while the length is increasing at a rate of 0m8 cm/hr. If the icircle is currently 4 cm in radius and 20 cm long. At what rate is the volume of the icircle increasing or decreasing?

Parcel changes of a courier company are as follows: P40 for the first 2 kilograms and P15 for each of the succeeding kilogram weight of the paecel With this rates, what amount would be charge for a 30 kg parcel?

Evaluate ln (3 + j4)

In Jones family, each daughter has as many brothers as sisters and each son has three times as many sisters as brothers. How many daughters and sons are there in the Jones family?

A man is paid P1,800 for each day he works and forfeits P300 for each day he is idle. If at the end of 40 days, he nets P53,100. How many days was he idle?

The polynomial x² + 4x + 4 is the area of a square floor. What is the length of its side?

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?

Of the coefficient a0 of a Fourier series of a periodic function is zero, it means that the function is

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

Describe the locus represented by | (z - 3i) | - | (z + 3i) | = 4

A runner runs in a circular track and a set of data is recorded: Time. Distance 68. 400 114. 600 168. 800 209. 1000 256. 1200 322. 1400 What is the average velocity from 68 sec to 168 sec?

A conic section whose eccentricity is less than one (1) is known as:

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

The geometric mean and the arithmetic mean of numbers are 8 and 10 respectively. What is the harmonic mean?

Find all the values for z for which e^4z = i.

What is the integral of sin5 (x) dx if the lower limit is 0 and the upper limit is π/2?

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

Find the unit vector orthogonal to both vectors 9i + 9j and 9i + 9k.

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

Find the volume generated by revolving the area bounded by y^2 = 12x and x = 3 about the line x = 3.

Praggnanandhaa and Magnus Carlsen got summer jobs at the ice cream shop and were supposed to work 15 hours per week each for 8 weeks. During that time, Magnus Carlsen was ill for one week and Praggnanandhaa took her shifts. How many hours did Praggnanandhaa work duringbthe 8 weeks?

The segment from (-1, 4) to (2, -2) is extended three times its own length. The terminal point is

Find the moment of inertia of the area bounded by the parabola y^2 = 4x and the line x = 1, with respect to x-axis.

The centroid of the area bounded by the parabola y^2 = 4ax and the line x = p coincides with the focus of the parabola. Find the value of p.

It represents the distance of a point from the y-axis.

The plate number of a vehicle consists if 5-alphanumeric sequence is arranged such that first 2 characters are alphabet and the remaining 3 are digits. How many arrangements are possible if the first character is a vowel and repetitions are not allowed?

From the 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 is 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.

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

From the top of a building the angle of depression of the foot of a pole is 48 deg 10 min. From the foot of a building, the angle of elevation of the top of a pole is 18 deg 50 min. Both building the pole are on a level ground. If the height of a pole is 4 m, how high is the building?

The equation y^2 = cx is a general solution of:

A political scientist asked the group of people how they felt about the policy statements. Each person was to respond A (agree), N (neutral) or D (disagree) to each NN, ND, NA, DD, DA, AA, AD and AN. Assuming each response combination us equally likely, what is the probability that the person being interviewed agrees with exactly one of the two policy statements?

Find the position value of c such that the area of the region bounded by the parabola y = x^2 - c^2 and y = c^2 - x^2 is 576.

Find the area bounded by y^2 = 4x and x^2 = 4y of the square in simplified form?

Find the centroid of the upper half of the circle x^2 + y^2 = 9.

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 ft/min?

Find the area enclosed by the hypocycloid of four cusps x = a cos3 (θ), y = a sin3 (θ).

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

Express in polar form: 3 - 4j

A rubber ball is dropped from a height of 81 m. Each time it strikes the ground, it rebounds two-thirds of the distance through which it last fell. Find the total distance it travels in coming to rest.

The area in the second quadrant of the circle x^2 + y^2 = 36 is revolved about the line y +10 = 0. What is the volume generated?

Two stones are 1 mile apart and are of the same level as the foot of the 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.

What is the vector which is orthogonal both to 9i + 9j and 9i + 9k?

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

Given sample space {2, 3, 7, 8, 11, 13, 16, 18, 20}. If 18 is mistakenly typed and if its value must be 16, which of the following changes value?

A bag contains 3 red, 6 blue, 5 purple and 2 orange marbles. One marble is selected at random. What is the probability that the marble is blue?

Find the area bounded by the curve defined by the equation x^2 = 8y and its latus rectum.

What is the area of the ellipse whose eccentricity is 0.60 and whose major axis has a length of 8?

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

A function f(x) is a (n) ___ function if f(-x) = -f(x).

The equations for two lines are 3y - 2x = 6 and 3x + ky = -7. For what value of k will the two lines be parallel?

What do you call a radical expressing an irrational number?

If Rita can run around the block in 5 times un 20 minutes, how many times can she run around the block in one hour?

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

A triangular fish pen has sides 30 cm, 50 cm, and 60 cm. Find the acute angle opposite to the shortest side.

Find the parametric equation for the line through the point (1,7,2) that is parallel to the plane x+y+z=10 and perpendicular to the line x=3+t, y=-18-t, z=5t

What is the shape of the graph of the polar equation r = a + bcos (θ)?

Integrate sqrt (1 - cosx) dx.

A man on a wharf 3.60 m above sea level is pulling a rope tied to a raft at the rate of 0.6 m/sec. How fast is the raft approaching the wharf when there are 6 m of rope out?

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 conic section whose eccentricity is less than one (1) is known as:

A steel girder 8 m long is moved on rollers along a passageway 4 m wide and into a corridor at right angles with the passageway. Neglecting the width of the girder, how wide must the corridor be?

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.

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

Hotels, like airlines, often overwork, 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?

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

A rectangle with sides parallel to the coordinate axes has one vertex at the origin, one on the positive x-axis and its fourth vertex is in the first quadrant on the line with equation 2x + y = 100. What is the maximum possible area of the rectangle?

Given is an 8 cm square. If the second square is made by connecting the midpoints of the sides of the first square and the third square is made by connecting the midpoints of the sides of the second square and this process continuous indefinitely, Find the sum of the perimeters of the squares.

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

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

A periodic waveform possessing half-wave symmetry has no ___.