Math 155 Formulas and Conversion Tables PDF

MATH 155 FORMULAS AND CONVERSION TABLES Updated Spring 2022 Metric Kilo Hecto Deka UNIT Deci Centi Milli Met...

MATH 155 FORMULAS AND CONVERSION TABLES Updated Spring 2022 Metric Kilo Hecto Deka UNIT Deci Centi Milli Meters Liters Grams LENGTH AREA VOLUME 1 in = 2.54 cm 1 ft2 = 144 in2 1 pt = 16 oz 1 ft = 30.48 cm = 0.3048 m 1 yd2 = 9 ft2 = 1296 in2 1 qt = 2 pt 1 yd = 91.44 cm = 0.9144 m 1 mi2 = 27,878,400 ft2 = 3,097,600 yd2 1 gal = 4 qt 1 mi ≈1.61 km 1 acre = 43,560 ft2 1 pt = 2 cups 1 mm ≈ 0.03937 in 1 mi2 = 640 acres 1 cup = 8 oz 1 cm ≈ 0.3937 in 1 gal = 128 oz 1 m ≈ 1.0936 yd = 3.2808 ft 1 in2 ≈ 6.45 cm2 1 km ≈ 0.6214 mi 1 ft2 ≈ 0.093 m2 1 ft3 ≈ 7.48 gal 1 yd2 ≈ 0.836 m2 1 yd3 ≈ 201.97 gal 1ft = 12 in 1 mi2 ≈ 2.59 km2 1 gal ≈ 231 in3 1 yd = 3 ft 1 acre ≈ 4,047 m2 1 ft3 fresh water ≈ 62.5 lb 1 yd = 36 in 1 ft3 salt water ≈ 64 lb 1 mi = 5280 ft 1 mi = 1760 yd 1 cm3 = 1 mL = 1 g = 1000 mm3 TIME 1 dm3 = 1000 cm3 = 1 L = 1 kg WEIGHT 1 min = 60 sec 1 m3 = 1000 dm3 = 1 kL = 1,000 L 1 lb = 16 oz 1 hour = 60 min 1 L ≈ 1.06 qt 1 ton (T) = 2,000 lb 1 day = 24 hours 1 ton (T) ≈ 0.9072 metric ton (t) 1 year = 365 days 1 gal ≈ 3.7854 L 1 qt ≈ 0.9464 L 1 kg = 1000 g 1 oz ≈ 29.5735 mL 1 metric ton (t) = 1,000 kg 1 ft3 = 1728 in3 1 kg ≈ 2.2 lb 1 yd3 = 27 ft3 1 oz ≈ 28 g 1 ft3 ≈ 0.02832 m3 1 yd3 ≈ 0.7646 m3 is % A % = = of 100 B 100 A B % Percentage = Rate * Base tip meal rate P=R*B part whole percent P is R% of B sales tax purchase difference original discount marked price commission total  𝑦2 − 𝑦1 5 9 𝑦 = 𝑚𝑥 + 𝑏 𝑚= 𝐶= (𝐹 − 32) 𝐹= 𝐶 + 32 𝑥2 − 𝑥1 9 5 𝑟 𝑛∙𝑡 Simple Interest: 𝐼 = 𝑃 𝑟 𝑡 Compound Interest: 𝐴 = 𝑃 (1 + ) 𝑛 𝐴=𝑃+𝐼 -or- 𝐴 = 𝑃(1 + 𝑟𝑡) 𝐴 Range: highest value – lowest value Present Value: 𝑃= 𝑟 𝑛·𝑡 (1+ ) 𝑛 Pythagorean Theorem: 𝑎2 + 𝑏 2 = 𝑐 2 Rectangle Square Parallelogram Triangle 1 𝐴 = 𝐿𝑤 𝐴 = 𝑠2 𝐴=𝑏h 𝐴= 𝑏h 2 𝑃 = 2(𝐿) + 2(𝑤) 𝑃 = 4𝑠 𝑃 = 2(𝑏) + 2(ℎ) 𝑃 = 𝑠1 + 𝑠2 + 𝑠3 Trapezoid Circle Cube Sphere 1 4 𝐴= h(𝑎 + 𝑏) 𝐴 = 𝜋𝑟 2 𝑉 = 𝑠3 𝑉= 𝜋𝑟 3 2 3 𝑃 = 𝑠1 + 𝑠2 + 𝑠3 + 𝑠4 𝐶 = 𝜋𝑑 𝑆𝐴 = 6𝑠 2 𝑆𝐴 = 4𝜋𝑟 2 -or- 𝐶 = 2𝜋𝑟 Rectangular Prism Cylinder Cone 1 𝑉 = 𝐿𝑤h 𝑉 = 𝜋𝑟 2 h 𝑉= 𝜋𝑟 2 h 3 2 𝑆𝐴 = 2𝐿𝑤 + 2𝑤h + 2𝐿ℎ 𝑆𝐴 = 2𝜋𝑟h + 2𝜋𝑟 2 𝑆𝐴 = 𝜋𝑟 + 𝜋𝑟√𝑟 2 + h2 Sum of measures for the interior angles of a n-sided polygon = (𝑛 − 2) ∙ 180° Properties of Exponents: 𝑎𝑚 𝑚 𝒏 𝑎 ∙𝑎 =𝑎 𝑚+𝑛 = 𝑎𝑚−𝑛 , 𝑎 ≠ 0 (𝑎𝑚 )𝑛 = 𝑎𝑚∙𝑛 𝑎𝑛 1 𝑎−𝑛 = ,𝑎 ≠ 0 𝑎0 = 1 , 𝑎 ≠ 0 𝑎𝑛