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Graphs and Functions

Equations and Graphing problems

Please show work so that I may understand. Thank you. 1.) Solve the equation x + 0.04x = 9600 2.) Solve the inequality (1/6) x - 1 ≤ 4 + (1/3) x. Express answer in both graphical and interval notation form. Find the missing coordinates y = -x + 4 x y -2 0 2 0 -2 3.) Plot

Graphing and Functions

1. Suppose I had a lemonade stand. When I charge $1, I sold 50 cups, when I raised the price to $2, I only sold 25 cups. Write an equation for the number of cups I sold as a function of the price i charged. Denote C for number of cups and P for price. Assume the function is linear. 2. Write an equation for f(x) based on x -2,

Discriminants

I am having trouble understanding the sign of the discriminant in quadratic equations. I'm confused. See attached for my full problem.

Slope-Intercept Form

Please show work so that I can understand how you arrive at your answer. Thank you. 1.) Write the equation in slope intercept form y + 2 = - 6(x-1) 2.) Determine the equation of each line. Write the answer in slope intercept form. The line through (4,0) that is perpendicular to the line x + y = 3 Solve

Outerplanar and Bipartite Graphs

A graph is outerplanar if it can be embedded in the plane so that every vertex lies on the boundary of the exterior region. A graph G is outerplanar iff G + K_1 is planar. Note:A bipartite graph (i.e., a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent

Graphs and the Time Value of Money

Please take this real-life situation: I currently have a CD investment accounts in the Dominican Republic. I invested $10,000 ($M) in The Central Bank of the Dominican Republic. This investment account produced a simple annual interest of 10% (R) for me. I plan to leave my money in this investment account for (X) amount of year

Critical Numbers : Find the intervals of increase and decrease.

Find the intervals of increase and decrease for a. Increasing on x -2 and x 8 , decreasing on - 2 x 8 b. Increasing on x < -8 and x > 2, decreasing on -8 < x < 2 c. Increasing on -8 < x < 2, decreasing on x < -8 and x > 2 d. Increasing on x < -2 and x > 8, decreasing on -2 < x < 8 An equation for the t

Which of the following represents a straight-line graph?

Please see attached file for full problem description. Which of the following represents a straight-line graph? a. none of the following is a straight-line graph b. all of the following are straight-line graphs c. varX varY 1 6 2 4 3 2 d. varW varZ 3 8 4 7 5 4 e. varT varU 10 0.5 11 1.5 12 2 Wh

Graphs and Minimizing Cost

Please see attached file for full problem description. Find constants a, b, and c so that the graph of the function has a relative maximum at (3, 7) and crosses the y-axis at (0, 1). Answer choices: , b = -4, c = -1 , b = 4, c = 1 , b = 4, c = 1 , b = -4, c = 1 Manufacturing company estimates

Solving Logistic Functions

The logistic growth function F(t)=600/1+11.0e^-0.16t describes the population of a species of butter flies t months after they are introduced to a non-theatening habitat. how many butterflies are expected in the habitat after 20 months? Rewrite the equation in terms of base e. Express the answer in terms of natural logari

Instantaneous Rate of Change

An object is moving along the straight line as follows. It starts at x = 0 and then it moves to the right to x = 2. Then the object moves to the left to x = - 3, and finally to the right to stop at x = 1. Sketch a possible graph of the position function s(t). Sketch a possible graph of the velocity v(t) (the instantaneous rate o

Graphing, Trends and Forecasting

Please see the attached file for the complete questions. Complete the ordered pairs so that each is a solution for the given equation. 24. (0, ), ( , ), ( ,0), ( , ) 46. Science and medicine. Celsius temperature readings can be converted to Fahrenheit readings using the formula . What is the Fahrenheit tempera

Graphing and Linear Equations

Please see the attached file for the complete questions. MTH 212 Unit 2 - Individual Project A 1. The following table shows the number of hours five car salespeople worked and the number of cars they sold. Using Excel, plot each point on the same graph where the first coordinate is the number of hours and the second coord

Over what intervals are the following functions continuous?

Please see attached file for full problem description. Over what intervals are the following functions continuous? Justify your answer using the definition of continuity. a. b. Let f and g be twice differentiable functions such that for all x in the domain of f. If and What (if anything) can you say about f,

Modelling Data with Polynomial and Rational Functions

Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileage at two different speeds, V1 and V2, the gas required varies as (V1/V2), raised to the third power, (V1/V2)3. Rational functions are also useful. For examp

Closed Loop Transfer Function

Please see the attached file for the fully formatted problems. Closed-Loop Transfer Function Find the state equation and output equation solution. Basically transfer from Transfer Function to State Space. Hint: Output Part of the answer has

Graphing an Eliipse and Interval Notation

Complete the square and sketch a graph of the following ellipse. Give the coordinates of the centre and the four vertices. What is the length of the major axis? 4x^2 + y^2- 8x + 4y -8 = 0 Solve and graph your solutions on the number line and express your answers in interval notation. 1. |3x - 7| >= 23 2. 1/2 |5-2x|

Applications of Graphs of Linear Equations

Name: __________________________ Date: _____________ 1. Which of the ordered pairs (6, 1), (8, 0), (4, -2), (-4, 6) are solutions for the equation x + 2y = 8? 2. A small company did a poll of how their employees commuted to work. The data is shown in the bar graph below. (a) How many people commute to work v

Trees, Graphs and Multigraphs

By contracting an edge e = uv, we mean removing e and identifying the vertices u and v as a single new vertex. Let num_T(G) denote the number of spanning trees of the graph G. a. Show that the following recursive formula holds: num_T(G) = num_T(G - e) + num_T (G * e) where G * e means the multigraph obtained from G by contrac

Graceful Trees and Paths

A (p,q) graph G is called graceful if it is possible to label the vertices of G with distinct elements from the set {0,1,...,q} in such a way that the induced edge labeling, which assigns the integer |i - j| to the edge ij, assigns the labels 1,2,...,q to the q edges of G. The graceful tree conjecture states that every tree i

Left-Side and Right-Side Continuous Functions

We define the floor function [[x]] to be the greatest integer not exceeding x. For example[[4]]=4 [[2.37]]=2 [[-1]]=1[[-1.2]]-2 Sketch by hand the graph y=[[x]] by first tabulating the values pf [[1]] for several numbers x. Then compare your graph with the plot from a graphing calculator. What are the discontinuities of f(x