1. For the following line elements and vector V", write down the metric, the inverse metric, and V² = 9μVHVV: dr² a) ds² = -(1 + r²) dt² + b) ds² = -drdy, V" = (V², V³) = (a, b) 1+r² +r²d0², VP = (V¹, Vr, Vº) = (a, b, c)
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- 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 notation1. 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…Can i get help with these problems pleasea. 2πR2+2πRh2πR2+2πRh b. 2πR2+2πh2πR2+2πh c. πR2hπR2h d. πD2+πDhπD2+πDh e. 2πR+2πRh
- a) Acceleration is described as space divided by time squared. Determine the dimensions of acceleration and its SI units.b) Kinetic Energy K has dimensions kg m2/s2. It can be written in terms of momentum p and mass m following the equation below. Determine the dimensions of the momentum and its SI units. c) The unit of force is the newton N, where 1 N = 1 kg m/s2. Determine the dimensions and the SI units of the momentum in terms of newtons.d) Newton’s law of universal gravitation is F =Gm1m2/r2 , where F is the magnitude of the gravitational force exerted by one object on another, m1 and m2 are the masses of the objects, and r is the distance between them. Determine the dimensions and the SI units of the proportionality constant G.1.3 The Role of Units in Problem Solving A particular convenience store offers a drink called the "MegaGulp". If the cup holds 107 fl oz. of liquid and we treat the "Mega" in the name as a metric prefix, how many mL are in a "Gulp"? O 0.000107 O 0.000000362 O 316000000 O 0.00317 Save for Later Submit Answer3] DETAILS ✔ m³/s (b) The surface area. 204 PREVIOUS ANSWERS x m²/s SCALCET9M 14.5.043. 3/5 Submissions Used The length , width w, and height h of a box change with time. At a certain instant the dimensions are l = 3 m and w = h = 8 m, and I and w are increasing at a rate of 5 m/s while h is decreasing at a rate of 4 m/s. At that instant find the rates at which the following quantities are changing. (a) The volume. 344 MY NOTES (c) The length of a diagonal. (Round your answer to two decimal places.) 4.33 x m/s ASK YOUR TEACHER PRACTICE ANOTHER