Math Problems and Solutions

Mathematics Problems and Solutions

• Area of the largest rectangle inscribed in 4x² + y² = 4 ellipse is 4.
• Radius increase rate when sand pours to make a cone with altitude twice radius when volume increases at 25π cu. ft./min and radius is 5 feet is 0.5 ft/min.
• Balloon 150 m from observer rises vertically. After one minute the angle of elevation is 28°59'. The angle after 3 minutes is 58°58'.
• Quarters needed for 2 candy bars, 1 peanut pack, and 1 cola can is 7.
• Ball dropped from 18m rebounds 2/3 of height. The total travel distance is 90 m.
• Limit of sin(x + 4 sin x) as x approaches 3π is equal to 0.
• Arc length of parabola x² = 4y from x = -2 to x = 2 is 4.6 units.
• Centroid coordinates of the area bounded by y = 4 - x² and the x-axis is (0, 1.6)
• Ways to pick 3 dogs from 7 dogs is 35.
• Ways 4 coins can be tossed is 16.
• Non-multiple of 11 among the options is 221.
• Shortest piece (5 inches) is 25% of the cut rope (8, 7, 5 inches).
• Length of each ribbon piece when 13.4 inches is cut into 4 equal pieces is 3.35.
• Volume generated when x² + y² = 36 in the 2nd quadrant revolves around y+10=0 is 2228.83.
• Distance of a point from the y-axis is the abscissa.
• In polar coordinates, a negative polar angle is measured clockwise.
• Coin tossed n times, 7 heads expected, coin tossed 14 times.
• Galvanized iron 60 cm wide bent into a trough; base width for maximum capacity is 20 cm.
• Nancy is 6 inches taller than Totoy.
• Time for Thomas to tie both shoes is 3.1 minutes.
• Volume generated by revolving ellipse 4x² + 9y² = 36 about the line x = 3 is 355.3.
• General solution of y² = cx has a derivative y' = y/2x.
• Solution to the differential equation y' = y/2x is y=cx.
• If 30% of high school is in athletics and 15% of athletes play football, 4.5% of the school plays football.
• Point on the line x=y=z equidistant from (3,0,5) and (1,-1,4) is (2,2,2).
• Number divisible by 6 is 792.
• Vehicle operating cost C(x) = 0.25x + 1600. For P5350 to P5600 spend, the travel distance is 15000 to 16000 miles.
• A 20-ft lamp casts a 25-ft shadow; a building casts a 50-ft shadow; the building's height is 40 ft.
• Largest angle of a triangle formed by connecting centers of three tangent circles (radii 3, 4, 5) is 73.4 degrees.
• Simplify cos² θ – sin² θ as cos 2θ.
• csc 520° is equivalent to csc 20°.
• Simplify x/(x - y) + y/(y - x) results in -1.
• Simplify (cos A) / (1- sin A) - tan A to sec A.
• Minimum distance from point (4, 2) to the parabola y² = 8x is 2 sqrt of 2.
• Standard deviation when 20 children recognize their mother's voice (90% success rate) is 1.34.
• Length of the side of an equilateral triangle inscribed in the parabola x² = 8y is 27.71.
• Mary is now 10 years old.
• If a cylinder has a lateral area of 77 sq cm and a volume of 231 cu cm, its radius is 6 cm.
• Fulcrum problem requires 36 pounds.
• Given an average of six scores is 83, and the average of five scores is 81.2, the removed highest score is 92.
• For x² - 4y² = 36, where x changes at 20 units/sec at point (10, 4), coordinate y changes at 12.5 units/sec.
• Given tan A = sqrt(3), with A in the 3rd quadrant, tan²(A/2) = 3.
• Stone projected upward at 112 ft/sec reaches a max height of 196 ft.
• Volume cut off from a cylinder radius 3 is 18.
• The diameter of the circle with center (2, 3) and passing through the point (-1, 5) is 7.2.
• Value of x for tangent to y = 4x - x² parallel to x-axis is 2.
• Surface area generated y² = x from x = 0 to x = 1 is 5.73.
• The number of students in the original group = 8.
• Allowable error for a cube of 8 cu. m. with a volume error not exceeding 0.03 cu. m. is 0.0025.
• y = 2x³ - 9x² + 12x - 2 has a maximum at x = 1.
• Distance from the airport light is 48,330 ft.
• Disappearance time of a substance decreasing inversely with rate of amount present (initially 12 units, 8 units after 2 days) is 3.6 days.
• Tower inclination angle = 7 deg 50 min.
• Telephones yielding largest profit = 15,000.
• Work done in moving an object along the vector a = 3i + 4j if the force applied is b = 2i + j is 10.
• Idle days = 7.
• Different Bracelets: 20,160
• Distance of center from chord = 12 cm.
• Slope is 1/5.
• The inverse of f(x) = sqrt(2x - 3) is (y^2 + 3) / 2.
• (g/f)'(3) = -58/49.
• The length of hypotenuse = 24 in.
• dy/dx for y = 3/(x^2+1) is -6x/(x^2+1)^2.
• Car angle of depression = 62 degrees.
• Find the area bounded by the curve r = 8cos θ which is 50.27.
• If 2log4 x - log4 9 = 2, then x = 12.
• Value of 2 cos(pi/4) = 2.65.
• The height of the pole = 15.8 m.
• Volume of a hemisphere = 16.76 cu. m.
• Five scores and 4 years is equivalent to 104 years.
• Equation of one asymptote for x² - 4y² - 6x - 8y + 1 = 0 is x - 2y - 5 = 0.
• The linear velocity is 75.4 fps.
• Solve the inequality 3 - 2x < 4x - 5 results x > 4/3.
• The polynomial x² + 4x + 4 is the area of a square floor, x + 2 is the length of its side.
• Computers needed is 30
• The distance between the two islands. = 220.5 km
• (x - y)¹? is 16.
• An equilateral triangle has sides of 8 inches the height is 6.93 in.
• Find the area of the triangle =12.45
• Find the moment of inertia of the area =25.6
• The rate cost of 1 dozen = Php 144.
• What is the amplitude of its motion =5 ft
• Evaluate z₁² + 2z₁ - 3. =-1-4i
• Identify the property of real numbers= Associative Property of Addition
• The distance between -9 and 19 on the number line =-28
• Find the mass of a 1.5-m rod: The answer is 4.5 kg
• The area bounded by the parabola: The correct answer is 2/3
• Find the coordinates of an object. The correct answer is (0, 4)
• Find the major axis of the ellipse The answer is 4
• What is its speed in meter per second? the right answer is 25
• The correct answer is 10
• the correct answer is 458
• Find b. The answer is -2
• The directrix is (x - 4)2 = -8(y-2) from the x-axis? the correct answer is 4
• Find the second derivative of y'= 1/X
• correct answer is 9.2
• Find the sum: 1094
• the final answer is 452.39 sq. in.