Configuring microphones, 692

Sound level of a leafblower, 230

Vibrating strings, 839

Air resistance, 1072

Direction of an airplane, 717

Paths of spacecraft, 743

Position of aircraft, 713

Speed and direction of aircraft, 703, 710, 722

Speed and direction of a bird, 722

Crop yields and fertilizer, 21, 281

Field enclosure, 898

Irrigation ditches, 889

Rate of a growing fruit on a tree, 153

Age of a fossil, 384

Amount of carbon left in ancient man found in ice, 386

Carbon dating of early human fossilized remains, 201

Window design, 327

Concrete needed to build a cooling tower, 469

of a sphere, 684

of an enclosed region, 678–681, 683–684, 692

Rate of change in its value, 183

Brightness of stars, 844

Density of a star, 971

Escape speed, 1008

Event Horizon of a Black Hole, 262

Modeling an asteroid, 962

Motion of planets, 804

Orbit of a comet, 689

Orbit of Mercury, 689

Planetary orbit, 688, 804

Searching for exoplanets, 861

Air flowing through a windpipe, 271

Bacterial growth, 1071

Chemical flow through bodies, 874

Yeast biomass as function of time, 296

Cost

of a box, 898

of manufacturing, 12, 14, 898

of materials, 889, 890, 895

of natural gas, 104

of production, 14

of removing pollutants from a lake, 128

postal rates per ounce, 80, 104

Manufacturing, 261, 886, 898

Maximizing profit, 887, 890, 898, 900–901

Minimizing cost, 901

Production of ball bearings, 234

Product production, 818, 857

Profit generated by unnamed technology, 296

Revenue of an unnamed commodity, 195

Sales, 153, 1069, 1071

Chemical reactions, 328

Crystals (structure of), 714, 698

Decomposition, 386

Decomposition reactions, 124, 129

Decrease of mass (glucose), 150

Energy within a system, 376

Growth of bacteria, 383, 385–386

Mixtures, 1087, 1096

Radioactive decay, 385, 386, 402, 1094

Salt solutions, 386

Rate of texting, 1071

Speed of a telephone call, 328

Graphics, 713

Minimizing cost, 327

of a box, 889

of a dam, 922

of a rain gutter, 270

of building a fence, 325

Supporting beam of a wall, 326

Christmas lights, 249, 274

Population growth, 253, 1087–1088, 1096

U.S. citizens, no High School diploma, 23

of a rare bird species, 535

Maximizing plot of land, 325

of a cylinder, 898

of a play area, 320

Ski slope, 443

Between cities, 670

Height of a building, 238

of an unnamed object, 260, 282, 286, 487, 519, 535

Traveled by a bee, 238

Traveled by a dropped ball, 560, 564

Traveled by motorcycle, 342

Cobb-Douglas Model, 838, 898

Demand equations, 153, 183

Margin of productivity, 839

Market penetration of smartphones, 207

Mean earnings for workers 18 years and older, 207

Price of tablets, 220

Production rates of unnamed commodities, 220

Rate of productivity, 833

U.S. Budget, 297

U.S. Economy, 342

Learning curve, 220

Student rating of faculty, 207

Test Scores, 80

Current in RL circuit, 307

Density of a current in a wire, 184

Drop in voltage, 386

Electrical charge, 732, 818, 1088

Electrical current, 162

Electrical field, 398, 818, 874

Electrical potential, 818

Flow over a cylinder, 1037

Height of a cable, 274

Kirchhoff’s Law, 1088

Magnetic effect on a TV, 1071

Magnetic fields, 818

Magnetism

of a cord, 733

of electrical charge, 732

of electrical current, 733

Parallel circuits, 848

Potential, 873, 874,

Rates of change for current, 177

Resistance, 207, 848, 860

Circuitry, 1072

Energy stored in a capacitor, 552

How calculators calculate, 634

Nuclear chain reactions, 552

Solar, 878

Amount of earth removed for a train to pass, 519

Bridges (St. Louis Arch), 249

Cable length, 444

Distribution of structural forces, 376

Electrical currents, 531

Electrical theory, 531

Length of hanging piece of rope, 444

Measuring ice depths, 901

River management, 403

Suspension, 246, 249

Wearing down of ball bearing, 233

Cable subscriptions, 326

Air quality, 1088

Disposal of pollutant, 143

Melting ice caps, 1096

Oil leakage, 261

Pollution in Gulf of Mexico, 1077

Field enclosure, 319

Consumer consumption, 564

Cost

of fuel, 273, 889

of health care, 412

of labor, 890

of mailing packages, 889

of mobile phone plans, 817

of natural gas, 92

of removing pollutant from a lake, 182

of water, 92, 104

Diminishing returns, 564

Flow of currency, 1088

Maximizing profits, 342

Present value of an unnamed currency, 531

Price of wine, 326

Projected business revenues, 191

Revenue maximization, 325

Sale of stereos, 342

Sales of an unnamed object, 293

Tax rates, 274

Gasoline in a tank, 456, 469

in a swimming pool, 456

in a trapezoid, 469

in a trough, 456

in a water tank, 469

on a dam, 456, 469

on a floodgate, 456

on a submarine, 456

in an oil tank, 456

Resultant, 455–456

Change in body temperature following death 398, 402

Longitude and latitude, 960

Area

of a circle, 155, 162, 377

of a disk, 238

of a rectangle, 260, 327, 342

of a triangle, 191, 469, 731, 847, 848

of an ellipse, 1011, 1055

enclosed by parabola, 970

of a parallelogram, 728, 731

Centroid, 1029

Cone volume, 327

Cube (volume of), 239, 252, 259

Cylinder (volume of), 238

Density of an unnamed object, 377

Dimensions of a box, 898

Dimensions of a rectangle, 322, 325

Equation of a line, 831, 860

Finding the center of a sphere, 962

Fractals, 564

Maximizing area of a triangle, 325

Parallelepiped (vectors), 714

Right triangle (area of), 352

of a river channel, 519

Snow ball (volume of), 260

Sphere (radius of), 260

Sphere (volume of), 238, 259

Surface area, 938, 940, 967, 968, 970, 1025–1026

of a balloon, 256, 260

of a bead, 661, 684

of a box, 818

of a catenoid, 660

of a circle, 970

of a cone, 660, 970

of a cylinder, 981, 989

of a dome, 940

of a helicoid, 1026

of a hemisphere, 940

of a horn, 660

of a paraboloid, 940, 970, 1056

of a plane, 939, 940

of a plug, 661, 684

of a pond, 519

of a searchlight reflector, 660

of a sphere, 260, 660, 939, 941

of a torus, 1024, 1026

of an unnamed solid, 658–659, 660, 682, 692

Tetrahedron (vectors), 714

Trapezoid (area of), 352

Triangle (area of), 260, 263, 327

Triangle (dimensions of), 260

Volume

of area removed from a sphere, 438

of a box, 898

of a circle drilled in sphere, 956

of a cone, 434, 438, 469, 1045

of a cube, 153

of a cylinder, 153, 438, 844, 847, 898, 926, 947, 971

of a liquid, 922

of a mountain, 955

of a paraboloid, 926, 968, 970

of a parallelepiped, 732, 1045

of a pyramid, 435, 437

of a silo, 848

of a solid, 469, 901, 909, 911, 919, 921, 923, 928, 929, 944, 948, 949, 953, 955, 959, 961, 968, 970

of a sphere, 162, 928, 961, 971

of a spherical cap, 962

of a tetrahedron, 922, 970

of a wedge removed from a cylinder, 437

of an ellipsoid, 949, 970

of ice, 857

of intersecting pipes, 438, 956

of water in a bowl, 437

of water in a glass, 437

of water in a tank, 929

Body mass index, 239

Human respiration rate, 153

Spread of an epidemic, 1085, 1087

Price of stocks, 564

Compound interest, 229

in CD’s, 230

center of, 955, 961, 970

intersection of two rods, 955

of a cone, 1055

of a cube, 949

of a cylinder, 949, 955

of fluid, 1040

of a plane, 932

of a solid, 935, 955, 961,

of a sphere, 955, 959, 961, 1037

of a square, 934

of a tetrahedron, 945, 949

of a triangle, 931, 934

of a washer, 935

of a wire, 980, 988, 989

Drug concentration, 183, 327, 361, 1071

Drug reaction, 531, 889

Radiation from x-rays, 338

Spread of a disease, 296, 564

Atmospheric pressure, 162, 207

Heat index, 817

Modeling a tornado, 1056

Temperature zones, 817

Path of a falling bomb, 171

Area of ground illuminated by a light, 328

Baking a potato, 102

Carrying a pipe around a corner, 328

Density of an object, 848

Fashioning a metal box, 319

Human intelligence, 629

Man walking in relation to the height of a tower, 260

Maximizing carry-on luggage, 898

Maximizing the volume of a box, 325, 341

Metal detectors, 890

Minimizing distance between two numbers, 327

Minimizing the surface area of a box, 325

Optimal dimensions for a can, 327

Optimal viewing angle for art on a wall, 327

Optimal wire length, 327

Path between two homes, 326

Weight lifting, 731

of a ball, 23, 179, 182, 338, 794

of a bullet, 206

of a car, 207, 791

of a dropped rock, 338

of a golf ball, 794

of hailstones, 207

of a harmonic spring, 129

of a hydrogen atom, 795

of an elevator, 184

of the Lunar Module, 196

of ocean waves, 191

of a pendulum, 1, 7, 32, 207, 238, 252

of a person walking and jogging, 152

of a piston in an automobile, 209

of a projectile, 274, 444, 650, 800, 801, 872

of a rocket, 398, 1072

of a spring, 37

of a subway train, 152

of a thrown rock, 335

of a train, 646

of an unnamed object, 112, 115, 182, 191, 195, 206–207, 220, 338, 367

of a wave, 857

of a weight on a string, 189, 191, 208

of water down a hill, 873

Path of a satellite in orbit, 818

Steering a boat, 722

Tracking an airplane, 262

Tracking a rocket, 261

Intensity of a light, 274

Light intensity, 327

Light passing through different materials, 324

Mirrors, 552

Camera distance calculation, 129, 239

Air resistance on a falling object, 398–399

Bodies in free fall, 341

Braking load, 722

Compressibility of gas, 220

Effect of elevation on weight, 238

Flow of liquid, 1034, 1035, 1036, 1037, 1056

Force

acting on a car, 807

acting on person in a car, 795

of an object dragged along the ground, 328

on an unnamed object, 518

needed to keep vehicle from skidding, 788, 794

Force fields, 1003, 1005, 1007, 1015, 1043

Frictional force, 1071

Gravitation/gravitational fields, 531, 818, 848, 874, 962, 977

Gravity (on Europa), 104

Harmonic motion, 274

Inertia, 338, 933, 935, 946, 949, 953, 954, 955, 961, 962, 970, 1015

Ideal Gas Law, 857

Kepler’s Laws, 804, 807,

Newton’s Law of Cooling, 1071

Newton’s Law of Heating, 1071

Potential of gravity, 874

Potential of magnets, 531

Proton in a particle collider, 794

Repelling charged particles, 1007

Snell’s Law, 848

Specific gravity of a sphere, 239

Speed of a thrown ball, 338

Speed of light, 629

Thermodynamics, 818, 838

Trajectory

of a baseball, 646

of a football, 646

Velocity

of a ball, 153

of a box sliding down an inclined plane, 341

of a circular disk, 208

of a falling object, 151

of a falling rock, 145, 147, 153

of a liquid through a tube, 171

of a thrown object, 102

of an automobile, 153, 162

of an unnamed object, 170, 184, 328

Water pressure against the glass of an aquarium, 495

Work

done by a chain, 451

done by a pulled rope, 446

done by a pump, 448–449, 451–452,

done by an electrical charge, 452

done by gravity on an unwinding cable, 451

done by horse pulling plow, 732

done by unnamed force, 1055

done to pull ore from a mine, 469

done to raise an anchor, 469

needed to lift a bucket, 451–452

needed to lift a rocket off the Earth, 452

needed to move a piston, 452

of an expanding gas, 452

pulling a cart, 713

pulling a wagon, 714, 722

pulling crates, 723

pushing lawnmower, 721

Ramp, 722

Tension in a cable, 714

to lift an elevator, 451

Tug of war, 714

Using a wrench, 731

Growth, 162, 183, 385–386, 402

of endangered bald eagles, 129

of insects, 128, 385

of the United States, 296

of wolves, 306

Stocking a lake with fish, 552, 564

Coin flips, 564

of cylindrical containers, 321, 325

Blood flow through an artery, 171

Change in light intensity on surface, 183

Change in light intensity through sunglasses, 192

Change in luminosity of the Sun, 171, 238

Change in the inclination of a ladder as it slips from a wall, 260–261

Change of angle of mirror as it slips on a wood floor, 191

Change of density in a diver’s body under water, 183

Change of gas pressure in a can, 183

Falling water level in cone, 260

of a baseball passing third base, 260

of a person rowing a boat, 326

of a person walking, 261

of a pile of sand increasing, 260

of a rumor spreading, 1087, 1096

of a turning searchlight, 262

of an unnamed object, 333

of change in a melting snowball, 340

of change in the angle of a rising balloon, 262

of corporate sales, 361, 367

of flowing water, 1072, 1081

of gas pressure changing, 261

of heated metal plate expansion, 261

of helium leaking from a balloon, 367

of miles per gallon, 326

of string being pulled by a kite, 261

of water being added to a reservoir, 367

of water released from a dam, 402

of weight change of an unnamed object in outer space, 262

Water leaking out of a pool, 171

Kinetic energy of an object approaching the speed of light, 130

of an aircraft, 105, 340, 713, 714

of a boat approaching a pier, 258

of a car 278, 282, 338, 377

of a child’s lengthening shadow, 261

of a decelerating car, 334, 338

of a downhill skier, 338

of a falcon moving away from its trainer, 261

of a person in a parachute, 1080

of a person riding a Ferris wheel, 261

of a rising container pulled by a pulley, 261

of a rotating lighthouse beacon, 340

of a shadow moving along a dome, 262

of a shadow moving along a wall, 263

of a skydiver, 306, 1087

of a train, 263

of a truck, 274

of a turning police searchlight, 262

of an unnamed object, 367, 377–378, 713, 730, 731, 1087

of elevator and delivery truck moving away from one another, 261

of engine pistons, 262

of falling hailstones, 129

of Mars orbiter, 794

of moving radar beam, 261

of rotation of lighthouse beacon, 259, 261

of satellite in orbit, 788

of sound, 839

of two vehicles moving towards one another, 261

of wind, 714

Baseball (bat’s center of mass), 465

Baseball (ERA), 817

Basketball (field goal percentage), 817

Golf (motion of a ball), 274

Golf (radius of water ripple if ball lands in a pond), 255

High jump on the Moon, 338

Mountaineering, 874

Races, 564

Swimming, 700, 722

Along an unnamed point, 818

Boyle’s Law, 860

Change in, 397, 832, 873, 874

Cooling time of a non–specific object, 128

Cooling time of a pie, 398

Distribution, 838, 839

Kinetic energy of gas, 92

of a metal plate, 868, 872, 900

of a rod, 376

of a sphere, 898

of an unnamed object, 395

Readings on a thermometer, 398

Change in volume of an open box, 262

of a ball, 239

of a balloon, 238

of a paper cup, 238

of a rain gutter, 327

of a tree trunk cut into logs, 513

of a trough, 327

of an unnamed revolving solid object, 478–479, 487, 495, 507, 519, 526, 531, 535

of expanding gas, 518

of gasoline in a tank, 3

of liquid in a cone, 20

of motor oil in a pan, 239

of water in a reservoir, 519

Rising water level in a cone, 260

Rising water level in a swimming pool, 257, 260

Rising water level in a tank, 260

Rainfall measurement, 376