University:
University of North Georgia
Course:
MATH 1450 | Calculus I
Academic year:

2024
Views:

356

Pages:

3
Author:

Autumn Cox

Question 1 A plastic rod is charged to -20 nC by rubbing. a. Have electrons been added to the rod or protons removed? Explain. b. How many electrons have been added or protons removed? Answer a) The rubbing is process in which the electrons are transferred between two materials. Initially two materials have equivalent or neutral charge. The process of rubbing, electrons are added to a material which is being rubbed whereas, electrons are removed from a material to get a negative charge which is rubbing. Therefore, the electrons are added to rod to make it negative charge and the negative sign indicates that electrons are more than protons. Thus, the electrons are added to plastic rod and reason is explained. b) Consider the expression for number of added electrons, q n= e 20nC 1.6 × 10-19 C 20 × 10-19 C 1.6 x 10-19 C = 1.25 × 1011 Therefore, the number of added electrons is 1.25 × 1011 Question 2 How many 3/4's are in 1? Answer To find how many 3 4 s are in 1, you need to divide 1 b by . To divide by a fraction, you must 3 4 rewrite is as multiplying by the reciprocal so 1÷ So 1 x 4 4 33 Since 3 3 4 4 = 1 x . Multiplying a number by 1 gives the original number 3 goes into 4 one time with a remainder of 1, then 1 then 1 three-fourths in 1. 3 4 1 as a mixed number is 1-. There are 3 3 Result: 1- 13 Question 3 A cylinder with a movable piston records a volume of 12.6L when 3.0 mol of oxygen is added. The gas in the cylinder has a pressure of 5.83 atm. The cylinder develops a leak and the volume of gas is now recorded to be 12.1 L at the same pressure. How many moles of oxygen are lost? Answer We know PV = nRT thus V is directly proportional to the moles ofgas(n) V₁ V2 thus use the formula n1 n2 12.6L/ 3mol = 12.1L/ x mol x=2.88mols this much moles of gas remaining Moles of gas lost = 3mol -2.88mol =0.12mol Question 4 The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and standard deviation. Ricardo spends less than one minute brushing his teeth about 40% of the time. He spends more than two minutes brushing his teeth 2% of the time. Use this information to determine the mean and standard deviation of this distribution. Answer "Table A contains the probabilities to the left of a z-score or for values smaller than z- score The time is less than one minute about 40% of the time. The time is more than two minutes about 2% of the time and thus less than two minutes about 98% of the time. 0.40 The z-value is then the value in the table A corresponding to a probability of : 0.98 z=-0.25 z= 2.05 The value is then the mean increased by the product of the z-value and the standard deviation. 1 = x = μ + 20 = μ – 0.250 2 = x = μ + 20 = μ + 2.050 Subtract the equations: 1 = 2.30σ Divide each side by 2.30: 0.4348 1 σ 2.30 Determine the mean: μ = 1 + 0.250 = 1 + 0.25(0.4348) = 1.1087 Result:µ = 1.1087. σ = 0.4348 Question 5 Find two sets A and B such that A∈ B and ACB. Answer Let A = {0} and B = {-{0},{1}}. A∈ B, -{0} is an elemnt of B. The empty set is a subset of every set, so A B as well. Answer is A = {0},B = {-{0},{1}}