Recall that if a function f of one variable is differentiable at x_0, it has a derivative at x_0 (via the limit definition of derivative). As one consequence, we know that f is continuous at x_0. This is not necessarily so in the case of a function of two or more variables. Consider the function: f(x,y) = (xy^2) / (x^2 + y^
Avoiding a collision. A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car's new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?
Central Limit Theorem Exercise Write a computer program or Excel spreadsheet that: a. takes a given distribution function (f(x), as given below), for x between: 0 and 1.0, b. randomly samples this function at n points and determines the mean for that sample c. repeats b. N times d. plots a histogram of the result of the
1. x+y=6 2. x-y=5 3. x-y=-3 4. x+y=-3 5. 2x+y=2 6. x-2y=6 7. 3x+y=0 8. 3x-y=6 9. x+4y=8 10. 2x-3y=6.
Trees can be used for many applications in computer science. One of these applications is decision-making, which is often used in the creation and analysis of databases. a) In one paragraph, define what trees are. Be sure to mention the difference between binary and n-ary trees. b) Represent the following hierarchical data
1. Create a Binary Relation between X and Y that contains at least 6 Ordered Pairs, given that X and Y are the following: Let the set X = {Bill Smith, Amos Black, Tarra Sigorney, Alfred Ross} Let the set Y = {MAT 102, ENG 202. PSY 303, BUS 405} 2. Given the following information, create the appropriate Digraph Let X =
For the function f whose graph is given (attached), state the value of each quantity, if it exists. If it does not exist, explain why. (a) lim (x->0) f(x) (b) lim (x->3-) f(x) (c) lim (x->3+) f(x) (d) lim (x->3) f(x) (e) f(3)
Let R(t) be the field of rational functions. Answer the following (with proofs): A. If we identify the rational numbers with a subset of R(t), what function corresponds to a given rational number r? B. Find a function f>0 in R(t) for which no rational number r satisfies 0 < r < f.
1. Find the slope of the line. 5y-4x+2=0 2.A line passes through the point (x,y) = (-2,-1) and has a slope of -2 . Write an equation for this line. 3. Write equations for the vertical and the horizontal lines passing through the point (-2,0) in (x,y)-coordinates vertical line= horizontal line= 4.Find the values of
The manager of a weekend flea market knows from past experience that if he charges x dollars for a rental space at the flea market, then the number y of spaces he can rent is given by the equation y = 200 - 4x. (a) Sketch a graph of this linear function. (Remember that the rental charge per space and the number of spaces rented
The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 mi and in June it cost her $460 to drive 800 mi. (a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. (b) Use part (a) to
1. Evaluate the difference quotient for the given function. Simplify your answer. (1) f(x)=x^3, f(3+h) - f(3)/h 2. Find the domain and sketch the graph of the given functions: a. F(x) = 1/2 (x+3) b. f(x) = {-1 if x< or equal to -1 3x+2 if abs(x)< 1 7-2x if x > or equal to 1
Using algebraic concepts to solve problems involving real data. World Population: A low-projection scenario of world population for the years 1995-2150 by the United Nations is given the function ... Flight of a Ball If a ball is thrown upward at 96 feet per second from the top of a building that is 100 feet high ... S
Indicate whether the given points below are on line 1, on line 2, on both line 1 and line 2, or on neither one of the two lines: Line 1: -4x -y+3=0 Line 2: 4x +3y -1=0 (x,y).............Line 1...........Line 2.........Both Lines..........Neither Line ( 1,-1) (2,-5) (4, 6)
Part 1...Find the slope and y intercept for the line if there is a slope and y intercept. x+2y=3 Determine whether the lines are parallel, perpendicular, or neither. y=x+7 y=-x+2
1.The demand function is: D(q) = 300/[4q+3] per unit. Find the total mount of money consumers are willing to spend to get 10 units of the commodity. 2. p= S(q) is the price (dollars per unit) at which q units of a particular commodity will be supplied to the market by producers, and q0 is a specified level of production. Fi
In our Learning-Team forum, we are to chose a graphing software/method and 'teach' it to the rest of the class. For this assignment, I have chosen the graphing software "Graph 4.x". As part of this assignment, we are to show how to start it, set it up, and how to graph functions (including parabolas and inequalities of 2 variabl
The number of new contributors to a public radio station's annual fund drive over the last ten years is 63, 58, 61, 72, 98, 103, 121, 147, 163, 198 Develop a trend equation for this information, and use it to predict next year's number of new contributors.
1. Construct a scatter plot using excel for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. Complete the table and find the correlation coefficient r. a. The data below are the ages and systolic blood pressure (measured in millimeters of mercury
The average SAT verbal score for students from one high school over the last ten exams is 508, 490, 502, 505, 493, 506, 492, 490, 503, 501 Write the equation of the trend line. Do the scores support an increasing or a decreasing trend?
2. Plot the graph of the equations 4x - 6y = 12 and x - 5y = 10 and interpret the result. 3. Plot the graph of the equations 8x - 4y = 12 and -4x + 2y = -6 and interpret the result. Figured out the other graphs these two just arent looking right. Not sure if I figured the equations out right with the methods used.
Week 4/2 Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as: 1. Integers 2. Rational numbers 3. Irrational numbers Week 4/ 3 1. How many solutions exist for a quadratic equation? How do we determine algebraically whether the solutions are real or complex? 2. Wh
A. Given f(x) = -3x + 7 1. Graph f(x). 2. Label the graph. B. Given f(x) = -3x2 + x - 5 1. Graph f(x). 2. Label the graph. Note: To draw the graph, you may use one or a combination of the following: - A spreadsheet program, such as Excel (*.xls) - A graphics program, such as Paint (*.jpeg, *.gif) - A word
A business student at Nowledge College must complete a total of 65 courses to graduate. The number of business courses must be greater than or equal to 23. The number of non-business classes must be greater than or equal to 20. the average business course requires a textbook costing $60 and 120 hours of study. Non-business cours
Please see the attached file for the fully formatted problems. MTH133 Name: 1) State the domain of the following and provide a brief explanation for your answer: a) Answer: b) Answer: c) Answer: d) Answer: e) Answer: 2) Suppose the graph of is shifted to obtain each the followi
MTH133 Unit 4 - Individual Project Name: 1) State the domain of the following and provide a brief explanation for your answer: a) Answer: b) Answer: c) Answer: d) Answer: e) Answer: 2) Suppose the graph of is shifted to obtain each the following graphs. What is the equation of
1. If line / goes through (1,3) and is parallel to the line through (4,3) and (-3,1). find the slope of /. 2. How do I write the equation y=2/3x-3 in standard form using only integers and a positive coefficient for x. 3. What is the equation if a line /goes through (-3,-1) and (-1,4)? 4. What is the equation in slo
Problem is attached as a word doc for readability purposes.
Need to provide a real world situation where the slope and intercept have some meaning in reality. The situation needs to describe what the dependent and independent variables are and what the slope and intercept means in terms of the real parameters.
Explain what makes a function a polynomial. Give an example of a function that is a polynomial and a function that is not a polynomial. Given the polynomial f(x) = 2x3 + 5x2 - x - 5, answer the following questions: Graph the polynomial. What is the degree of the polynomial? Explain the constant in the polynomial and how