A circle of radius of 8 cm is inscribed in a sector having a central angle of 80°. What is the area of the sector?

Determine the number of possible triangles that can be formed given the following measurements: <A=110°, c=19cm, a=32 cm

What is the future worth of P600 deposited at the end of every month' For 4 years if the interest rate is 12% compounded quarterly?

Compute the center of mass of the region bounded by y = cos(2x), x = -π/4, and x = π/4.

Water is running into a hemispherical bowl having a radius of 10 cm at a constant rate of 3 cm3/min. When the water is x cm. deep, the water level is rising at the rate of 0.0149 cm/min. What is the value of ‘x’?

Suppose the heights H of 800 students are normally distributed with mean 66 inches and standard deviation 5 inches. Find the number N of students with heights between 65 and 70 inches.

A company is considering two types of equipment for its manufacturing plant. Pertinent data are as follows: Туре А Type B First cost 200,000 300,000 Annual operating cost 32,000 24,000 Annual labor cost 50,000 32,000 Insurance and property taxes 3% 3% Payroll taxes 4% 4% Estimated life 10 10 If the minimum required rate of return is 15%, which equipment should be selected? Use the present worth analysis. Hint: Payroll tax = Labor Cost * Payrol1%, Insurance and property tax = FC x I&P%.

What is the area bounded by the curve y = x3, the x-axis and the line x = –2 and x = 1?

A solid figure is in the shape of a two-base spherical segment with the upper base being the great circle of radius 5. Its capacity is 66π. What is the total surface area of figure?

There are 10 points in a plane. No three of these points are in a straight line, except 4 points which are all in the same straight line. How many straight lines can be formed by joining the 10 points?

A man walks from his house to the office. If he leaves at 8:00 o’clock and walks at the rate of 2 kph, we will arrive 3 minutes earlier, but if he leaves at 8:30 and walks at 3 kph, he will arrive 6 minutes late. What time should he arrive at the office?

A pole cast a shadow of 15 meters long when the angle of elevation of the sun is 61°. If the pole has leaned 15° from the vertical directly toward the sun, what is the length of the pole?

Two spheres each a 9.6m diameter are melted down and recast into a square pyramid with a height equal to the side of its base. Find the height of the pyramid.

If an open box is to be made using a square sheet of tin, 10 inches by 10 inches, by cutting a square from each corner and folding the sides up; find the length of a side of the square being cut so that the box will have a maximum volume.

Find the probability that in five tosses of a fair die, a 3 will appear at least two times.

A balloon is released from the ground 100 meters from an observer. The balloon rises directly upward at the rate of 4 m/s. How fast is the balloon receding from the observer 10 seconds later?

The edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

Minari’ is the name of an earth satellite that has an apogee of 2450 miles and a perigee of 410 miles. Assuming that the earth’s radius is 400 miles, what is the value of the eccentricity of the ellipse formed with the center of the earth at one focus and whose apogee and perigee satisfy the condition presented by this problem?

Find the moment of inertia, with respect to the x-axis of the area bounded by the parabola y2 = 4x and the line x = 1.

The NationalGovernment intends to build a dam and hydroelectric project in 12.Valleyat a totalcost of P455,500,000.The project will bethe Cagayan financed by a soft foreign loan with a rate of interest of 5% per year. The annual cost for operation,maintenance, distribution facilities, and benefits are estimated to bewould total P15,100,000. Annual revenues structures are expected to last for 50 years with no P56,500,000. If salvage value, determine the B/C ratio of the project

A boatman is at A which is 4.5 km from the nearest point B on a straight shore BC. He wishes to reach in minimum time a point C situated on the shore 9 km from B. How far from C should he land if he can row at the rate of 6 kph and can walk at the rate of 7.5 kph?

A camera on the ground 200 meters away from a hot air balloon records the balloon rising into the sky at a constant rate of 7.3 m/sec. How fast in degrees/sec is the camera’s angle of elevation changing when the balloon is 150 m in the air?

If two brown-eyed parents have a blue-eyed child, then the parents must each have one blue- and one brown-eye gene. To have blue eyes, the child must get the blue-eye genes from both parents. What is the probability that two brown-eyed parents can have two children, all with blue eyes?

Hev Abi borrows P600,000 at 12% compounded annually agreeing to repay the loan in 15 equa annual payments. How much of the original principal is still unpaid after he has made the 8th payment?

A trough is 20ft long, and its ends are isosceles triangles that are 5 ft. across the top and have a height of 2 ft. If the trough is being filled with water at a rate of 9 ft3/min, how quickly is the water level rising when the water is 1 foot deep?

The kinetic energy E of a body is proportional to its weight W and to the square of its velocity v. An 8-lb body moving at 4 ft/sec has 2 lb–ft of kinetic energy. Find the kinetic energy of a 3-ton (6000 lb) truck speeding at 60 mi/hr (88 ft/sec)

Find the minimum amount of tin sheet (in in2) that can be made into a closed cylinder having a volume of 108 in3

FlOw G purchased a small lot in a subdivision, paying P200,000 down promising to pay P15,000 every 3 months for the next 10 years. The seller Tirured anterest at 12% compounded quarterly. If Flow G missed the first 10 payments, what must he pay when the 11* payment is due to discharge his entire indebtedness?

A 6-ft-tall person walks away from a 10-ft lamppost at a constant rate of 3 ft/sec. What is the rate at which the tip of the shadow moves away from the person when the person is 10 ft from the pole?

Find the volume of a right circular cylinder whose lateral area is 25.918 m2 and base area of 7.068 m2

When area of a square is increasing 4 TIMES as fast as its diagonals, what is the length of a side of the square?

The side of a square sheet of metal is increasing at 3 cm/min. At what rate at 34 is the area increasing when the side is 10 cm long?

A helicopter is rising vertically from the ground at a constant rate of 4.5 m/s. 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 changes after 1 second.

Two points on a circle are subtended by another point on the circle with an angle of 51°. If the radius of the circle is 8, what is the shortest distance between the two points along the circle?

A light on the ground 100 feet from a building is shining at a 6-foot-tall man walking away from the streetlight and towards the building at the rate of 2 ft/sec. How fast is his shadow on the building growing shorter when he is 40 feet from the building?

A spherical balloon is being filled with air at the constant rate if 2 cm^3/sec. How fast is the radius increasing when the radius is 3 cm?

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?

What is the integral of sin5xdx if the lower limit is 0 and the upper limit is π/2?

Find the area of the region bounded by y2 = 8x and y = 2x.

Two identical cones with vertical axis, one inverted and the other is upright having base radius of 1.2 m and height of 4.8 m. Each cone contains an equal volume of oil having a specific gravity of 0.80. If the depth of oil in the inverted cone is 2.4 m., what is the depth of oil in the upright cone?

Find the surface area of a sphere at the instant when the rate of increase of the volume of the sphere is seven times the rate of increase of the radius.

A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 6 feet across at its opening and 3 feet deep at its center, at what position should the receiver be placed? That is, where is the focus?

Integrate the square root of (1–cosx)dx.

A closed cylindrical tank of maximum volume is to be constructed. With only 381.7 m^2 of material, what will be the tank’s height in meters?

Find the volume generated when the plane area bounded by y = -x^2 - 3x + 6, x + y - 3 = 0 is revolved about y = 0.

A right regular hexagonal prism is inscribed in a right circular cylinder whose height is 20 cm. The difference between the circumference of the circle and the perimeter of the hexagon is 4 cm. Determine the volume of the prism.

A six-faced fair dice is siled five times. The probability (in 8) of obtaining “ONE” atleast four times

Find the volume of the area bounded by the graph of 4x^2 + 9y^2 = 36 within the first and second quadrant about the x-axis.

The Golden Gate Bridge, a suspension bridge, spans the entrance to San Francisco Bay. Its 746-foot-tall towers are 4200 feet apart. The bridge is suspended from two huge cables more than 3 feet in diameter; the 90-foot-wide roadway is 220 feet above the water. The cables are parabolic in shape* and touch the road surface at the center of the bridge. Find the height of the cable above the road at 1266.4 feet from the center.

The angle of elevation of the top of an incomplete lighthouse at a horizontal distance of 120 m. from its base is 38°. The angle of elevation of the complete lighthouse measured from the same point is 68°. The height of the incomplete tower is increased by how much?

A piece of wire having a total length of 72 cm was cut into two unequal segments and bent to form two unequal squares. If the total area of the squares is 180 cm2, what is the difference in the lengths of the two segments?

A man in a rowboat, 6 miles from the nearest point A on a straight shore, wishes to reach a point B, 5 miles from A along the shore, in the shortest time. Where should he land if he can row 2 mi/h and walk 4 mi/h?