A tangent to a conic is a line which

What is the conic section whose eccentricity is equal to 1?

If y-arctan (lnx), find y' when x-1/e

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.

In polar coordinate system, the polar angle is negative when

A 6-ft pine tree is planted 15 feet from a lighted streetlight whose lamp is 18 ft above the ground. How many feet long is the shadow of that tree?

In the curve 2+12x-2x³, find the critical points.

Find the area bounded by the parabola x²-2x+2y+5=0 and x²-2x+y+1=0

The graph represented by the polar equation r=a+b cos theta is

A transmitter with a height of 15m is located on the top of a mountain, which is 3km 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.

The axis of the hyperbola through its foci is known as

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

The area bounded by the curve y²=12x and the line x=3 is revolved about the line x=3. What is the volume generated?

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

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 choosen is blue?

Find the volume in cubic units generated by rotating a circle x²+y²+6x+4y+12=0 about the y-axis.

A cone shape 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 0.8 cm/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?

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

Water is running out of a conical funnel at the rate of 1cu. in/sec. If the radius of the base of the funnel is 4 inches and the altitude is 8 inches, find the rate at which the water level is dropping when it is 2 inches from the top.

A man on an observation sees a fire directly south of him. A boy on another tower 20km east of the first tower observes the fire at a bearing S 40°15' W. What is the distance of the first tower from the fire?

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

What is the conic section x²+6x-y+12=0

What's the equation of the hyperbola with a focus at (-3-3sqrt. of 13, 1) asymptotes intersecting at (-3, 1) and one asymptote passing thru the point (1,7)?

Find the radius of the circle inscribed in the triangle determined by the lines y=x+4, y=-x-4 and y=7x-2.

If the radius of the sphere is increased by a factor of 3, by what factor does the volume of the sphere change?

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

If log x base 64 is 3/2. Find X.

A chord of a circle is 10ft in diameter is increasing at the rate of 1ft/s. Find the rate if change of the smaller arc subtended by the cord when the cord is 8ft long.

Find the equation of the family of orthogonal trajectories of the system of parabolas y²=2x+C

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

From the past experience, it is known 90% of one-year old children can distinguish ther 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.

A bus leaves Manila at 12 NN for Baguio 250 km away traveling an average of 55 kph at the same time, another bus leaves Baguio for Manila traveling 65 kph. At what time will they meet?

A statistic department is contracting alumni by telephone asking for donations to help fund a new computer laboratory. Part 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 between 14 to 18 alumni will make a contribution at least P50.00?

Jun rows his banca a river at 4km/hr. What is the width of the river of he goes at a point ⅓ km downstream?

Find the surface area generated by rotating the parabolic arc y²=X about x-axis from x=0 to x=1

There are four geometric mean between 3 and 729. Find the sum of the geometric progression.

In a hotel it is known that 20% of the total reservation will be cancelled in the last minute. What is the probability that these will be fewer than 2 reservation cancelled out of 4 reservation?

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

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 of 8kph in order to go a given distance most economically?

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

When two lines are perpendicular, the slope of one is

The volume of a cube becomes three times when its edge is increased by 1 inch. What is the edge of the cube?

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

All circles having the same center but with unequal radii are called

A point is choosen at random inside the circle of diameter 8in. What is the probability that it is at least 1.5 inches away from the center of the circle.

The three sides of a trapezoid are each 10m long. How long must the fourth side be to make the area a maximum.

A political scientist 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, NA, DD, DN, DA, AA, AD, and AN. 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?

In the 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?

A high school band teacher has a record of each student's attendance. The results is listed below in days each student has been absent. 3. 4. 7. 2. 2. 1, 0, 0, 1, 0, 3. 3. 2. 1, 6, 0, 1, 0, 1, 1, 1, 5. 3. 1, 1, 0, 0, 2. 1, 2, 1, 0, 0, 4 What proportion of the students have been absent less than 3 days?

A line through (0, 0) intersects y=x2 at a point (a, a2). The area of the upper region bounded above by the line and below the curve is 27.

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 percentage of the students spends between 6.5 and 8.5 hours learning the software package?

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 15 questions. How many questions should the student expect to answer to answer correctly?

In two intersecting lines, the angles opposite to each other are termed as: