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Graphs and Functions

Equation of a line

The following information regarding a dependent variable Y and an independent variable X is provided. SumX = 10 SumX^22 = 30 SumY = 10 SumY^2 = 30 SumXY = 20 n = 4 Find the equation of the line.

Evaluate the amplitude, period, and phase shift of the function.

Show how certain problems can be worked. Please see the attached file. 1) Find the exact value of the sine, cosine, and tangent of the number, without using a calculator. -13π/4 sin (-13π/4) = cos (-13π/4) = tan (-13π/4) = 2) Find sin (t), cos (t), tan (t) when the terminal side of an angle of t radians in stan

Analysis

Consider a function fâ?¶[0,1]â?'[0,1] given by f(x)={(1/q, if x=p/q,where p,qâ??N are coprime, 0, if x is irrational, 1, if x=0. (a) Show that if xâ??[0,1] is rational, then f is not cont

Differentiable and continuous functions

Suppose fâ?¶Râ?'R is twice differentiable with both f' and f'' continuous in an interval around 0. Suppose further that f(0)=0. Let h(x)={f(x)/x, if xâ? 0, f^' (0), if x=0. Show that (a) h is differentiable at x=0. (b) h is differentiable at x=0 with h^' (0)=1/2 f^'' (0). (c) h' is continuous at x=

Equation of parabola and ellipse in standard form

5.Given the equation of the parabola( x^2)+4x-8y+4=0 (a)Write the equation in standard form (b)Find the coordinates of the vertex, focus and equation of the directix. 6.Given the equation of the ellipse (9x^2)+(4y^2)-36x+8y+31=0 in standard form and find the center, foci, and vertices. Sketch the graph clearly labeling

Properties of a given bipartite graph

For this question, let G = K9,10: (a) The number of vertices in G is (b) The number of edges in G is (c) The number of components in G is (d) The number of hamiltonian cycles in G is (e) λ(G) = (f) k(G) = Confusing in part e and f. plz show all you work and answer. thx

Quartic or Quadratic Polynomial Functions

1.For the following graph: Suzanne suggests that the graph is most likely a quadratic function. Simon disagrees, as he believes that the function must be a quartic function. Who is correct? Explain. 2. Graph each function given below on a graphing calculator to find a general rule for determining when a graph crosses the x

Motion Graphing: Distance vs Time

** Please see the attached file for the complete problem description ** Given a distance vs. time graph (see below), make up a scenario that the graph could describe. Label the graph to depict what is happening and where you are in the scenario. Be as specific as possible.

Evaluate the Linear Function

Answer the following questions. Show your calculations. 1. Evaluate the function f(x) = 9x - 6 for x=0. 2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the l

Principal ideal domain

Let R be a principal ideal domain and a, b, in R, not both zero. Prove that a, b have a greatest common divisor that can be written as linear combination of a and b. Hint: let I be the ideal generated by a and b, then I = (d) for some d in R. Show that d is a gcd of a and b.

Horizontal and vertical line on a polar curve

Find the points on the given curve where the tangent line is horizontal. Find the points on the given curve where the tangent line is vertical. r = e^theta where theta is between zero and 2 pi.

Mathematics: Linear Graphing

Plot (x,y) points on graph and identify slope using mathematical concepts rise/run and Y=mx+b -. Please show example of steps to take to identify (x,y) coordinates in order to plot on a line graph, as well as steps taken to identify the slope. Here's info I have: Year (x) Temp (degrees Celsius) (y) 1950 13.83 19

determine the objective function

1. Define the decision variables and determine the objective function for the following problem. Consider the following transportation problem: To (cost) From 1 2 3 Supply _____________________________________________ A

Convex & Concave Functions

Which of the following is the complete set of numbers for which the function f(x) = 3x^3-6x^2 is convex? a. x is less than or equal to 0 b. x is greater than or equal to 0 c. x is less than or equal to 1 d. x is greater than or equal to 1 e. none of the above.

Set of all bounded functions is complete

(X,d) set of all bounded functions on X prove that (B(X), is a metric space B(X) is the h) is complete where h is the metric h(f,g) = sup{If(x)-g(x)I, x in X} Edit If(x)-g(x)I means the absolute value of f(x)-g(x)

Find the singular part for the function z^2+1/z(z-1)

The following function f has an isolated singularity at z=0. Its nature: it is a pole; find the singular part. f(z)=(z^2+1)/(z(z-1)) Use this equation and definition: Equation: f(z)= A_m/(z-a)^m +⋯+ A_1/((z-a) )+g_1 (z) (*) Where g_1 is analytic in B(a;R) and A_m≠0. Definition: if f has a pole of order m at z=0 a

Measurable Functions

Prove directly from Proposition 17.2 that each of the following function is measurable on [0,1]. a) f(x)=3 for all x in [0,1] b) f(x) =x for all x in [0,1] c) f(x)=1 if x in (0,1], f(x)=0 if x=0. I have also included the proposition in the attachment Thank you

Optimal Value of the Objective Function

Consider the following linear programming problem: Max 8X + 7Y s.t. 15X + 5Y < 75 10X + 6Y < 60 X + Y < 8 X, Y ï?³ 0 a. Set up and solve using Management Scientist, Excel Solver, or an online LP solver. b. What are the values of X and Y at the optimal solution? c. W

Quanatative methods

Your companym Camel Electronics has developed a new USB memory device that uses a copyrighted, secret silicon compound that you invented. The 640 gigabyte model uses 0.125kg of the compound and the 1 Terabyte model uses 0.4. Over the next production cycle, only 80 kg of the compound are available to the manufacturing division

Graph

Graph each line and shade appropriate portion . for every case there constrains x â?¥ 0 and y â?¥ 0 . Find coordinates of all corner points: intersection between given lines and intersection between lines and x- or y-axis . x + y â?¤ 5 -x + y â?¤ 3

Apply graphing technique to find solutions.

Use graphing technique to find solutions 1. 3x - 4y ≤ 12 2. 2x + y ≤ 4 3. 5x - 3y ≥ 15 4. x + y ≥ -2 x - 2y ≤ 4 5. x + y ≤ 4 0 ≤ x ≤ 2 y ≥ 0 6. 3x + 4y ≤ 12 x - y ≤ 4 x ≥ 0 Draw the line, use (0,0) test to find on what side of the line is the solution and shade

Piece wise defined function

Not: this is a piece wise defined function x^(2) + 5, if x<b Let f(x) = d, if x=b x^(2) - 8x, if x>b a) Find b such that lim f(x) exists. x->b Note: Enter does not exist if no b exists which make the limit well defined. b=_________ b

The slope of the secant line

Consider the function f(x)= sqrt(7x+6) We will take steps to find the tangent line to the graph of f at the general point (x,f(x)), and use it to find a tangent line with a specific property. (a) For any point (x,f(x)) on the graph of f, let (x+h,f(x+h)) be another point on the graph of f, where h [cannot]= 0 . The slope

Solving, drawing the graph and explaining

4. Determine whether the following linear programming problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion. Maximize 20x + 5y Subject to: 2x + y > 15 x + y < 5 y < 5 x, y > 0

Point slope form for an equation

Use the point-slope form of the linear equation to find an equation of the line with the given slope and passing through the given point. Then write the equation in standard form. Slope -2/3; through (4,5)

verbal description of the variation

The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the speed and inversely as the radius of the curve. it takes 3000 pounds of force to keep a 2000 pound car from skidding with radius 400 at 40mph. What force is needed to keep the same car from skidding when it tak

Blocks of a given graph and expansion to a 4-critical graph

For n∈N, let G be the graph with vertex set {v_0,...,v_3n} defined by v_i↔v_j if and only if |i-j|≤2 and i+j is not divisible by 6. a) Determine the blocks of G. b) Prove that adding the edge v_0 v_3n to G creates a 4-critical graph.

range of scores on the final exam

The professor counts his midterm as 2/3 of the grade and his final as 11/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put her average between 70 and 79 inclusive?

Linear Equations and Slope

1. given the following equation, 5x - 3y = 15; solve for y. 2. Verify that the ordered pair (5, -2) is a solution to the equation 2x + 3y = 4 3. for the following equations: 5x - 2y = 14: find x if y = 4 find y if x = 2/5 4. find the slope and the y-intercept of the line represented by the equation: 2x + y =