1. Write the following using the summation convention. (i) ¢!)² + (x²)² + (x³)² + · …+ (x")²
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- Using the formula for the sum of consecutive integers, compute the following. 11 E, 2i = i=1 11 Σ2- 11 E(2i + 3) =2abQ1) A) Find the answers to the following problems using the rule of Significant Figures a) (10.4168) m - (6.0) m b) (1.31) ст х (2.3) сm c) (5.7621) m / (6.201) m d) (2.5000) m + (32.85) m B) Represent each answer above in the scientific notation
- 1. Multiplication or division: keep the same number of significant figures in the product or quotient as is in the least precise factor. Examples: 3.1 * 25.6=79.360000... = 79 6.7/981.0=0.0068297655... = 0.0068 keep only 2 significant digits 2. Powers or roots: keep the same number of significant figures as in the original number. Example: Sqrt(38) 6.164414... keep only 2 significant digits = 6.2 (11.6)² = 134.5600000... = 135 Exercises 3. Addition or subtraction: Round off, to the number of decimal places determined by the number with the least number of places beyond the decimal point. Example: 31.5+24.61 +3.28+1.19 +0.762 +0.003 = 61.345 1. 3.9 * 78.9= = 61.3 (correct result) 2. 32.01 +96.321 +36.98 +0.00023 +28.9= 3. 26.9/98 = 4. 421 0.003 =Practice) a. To convert feet (ft) to meters (m), the number of feet should be multiplied by which of the following conversion factors? i. 1 m/3.28 ft ii. 3.28 ft/1 m b. To convert sq.in to sq.ft, the number of sq.in should be multiplied by which of the following conversion factors? i. 144 sq.in/1 sq.ft ii. 1 sq.ft/144 sq.in c. To convert sq.yd to sq.ft, the number of sq.yd should be multiplied by which of the following conversion factors? i. 1 sq.yd/9 sq.ft ii. 9 sq.ft/1 sq.yd 3. (Practice) Determine the final units of the following expression: 9.8m/s2 ×100cm/1m×1in/2.54cm×1ft/12in 4. (Practice) a. Determine the conversion factors that can be used to convert miles per gallon (mpg = mi/gal) to kilometers per liter (km/liter), given that 1 liter = 0.22 gallons and 1 kilometer = 0.6214 miles. b. Using the conversion factors you determined in Exercise 4a, convert 25 mpg into km/liter. 5. (Automotive) a. An automobile engine’s performance can be determined by monitoring its rotations per…a. 2πR2+2πRh2πR2+2πRh b. 2πR2+2πh2πR2+2πh c. πR2hπR2h d. πD2+πDhπD2+πDh e. 2πR+2πRh
- Find the number of significant figures in each of the following. (a) 61.8 ± 0.3 (b) 3.86 ✕ 109 (c) 2.80000 ✕ 10−6 (d) 0.0045Question 3 We can model a human as a cylinder with a height of 1 m and a radius of 10 cm. Which is the best order of magnitude estimate for the number of cells in a human body? O 10^13 O 10^11 O 10^7 1019 O 10^15Simplify the expressions. (a) −(25 + 12) (b) −7 − (6 − 3)