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Graphs and Functions

Exponential function

Why does the graph of the basic exponential function lie entirely above the x-axis?

Horizontal asymptotes and costs

How could you interpret infinity in the y values for costs, a negative x value for time, or a horizontal asymptote in y values for profits?

Graphing question

What is the solution to a system of 2 equations represented by 2 parallel lines in the same plane?

Resultant force

A=(310 LBS, 37DEGREES), B=(267 LBS, 348DEGREES), C= (148 LBS, 247DEGREES), D= (139 LBS, 167DEGREES) Determine the resultant force by the component method.

Resultant force

Find the resultant force (sum) of these displacements: 400 mi, EAST: 200 km, EAST: 400 km : AND 100mi, NORTH.

Forces

A steel beam exerts a force of 350 lbs against a wall at a 60 degree angle from vertical. What is the horizontal component of this force acting perpendicular to the wall?

Resultant force

What are the vertical and horizontal forces of a 1200 N force directed to the right and upward at an angle of 43 degrees with the horizontal?

Riemann Integrable Function : Upper and Lower Sums

Please see attachment. Q. Show directly that the function is integrable on R = [0,1] x [0,1] and find (Hint: Partition R into by squares and let N , limUp = limLp = integrable Up = upper Riemann sum of f respect to partition  U(f,p) = Lp = Lower Riemann sum of f respect to partition  L(f,p) =

Vector Components : Force

A FORCE OF 85 N ACTS TO THE LEFT AND DOWNWARD AT AN ANGLE OF 45 DEGREES WITH THE HORIZONTAL. WHAT IS THE EFFECTIVE DOWNWARD FORCE AND WHAT COMPONENT IS ACTING TO THE LEFT?

Chromatic Number; Planar

Use words to describe the solution process. No programming. 2. Let G = (V,E) be a graph where V {1,2,3,4,5,6,7,8,9,10,11,12} and E contains all edges connecting to vertices a and b such that ab=0 (mod 3). What is the chromatic number of G? Is G planar?

Graph Coloring Problem

Please use words to describe the solution process: Let G be a graph with exactly one cycle. Prove that x(G) is less than or equal t0 3. *(Please see attachment for proper symbols)

Graph Coloring Problem

Please use words to describe the solution process: Let G be a graph with n vertices that is not a complete graph. Prove that x (G) < n HINT: If G does not contain k3 as a subgraph, then every face must have degree at least 4. *(Please see attachment for proper symbols)

Graph Coloring Problem

Please use words to describe the solution process. Let G and H be the graphs in the following figure (see attachment): Please find x(G) and x(H).

Evaluate the Binomial Coefficient

Evaluate the combination or binomial function in the completion 48 factorial over 37 factorial. The answer should equal to 22595200368.

Need to graph equation where x = -2

I must write an equation that has the solution x = -2 and graph it. My equation must include combining like terms on the left side and distributive property on the right side. I missed two weeks of class due to illness, and am having a hard time working this out. I just need a sample answer or starting point so that I underst

Differential Equations

27. y'' + 25y = sin(4t), y(0) = 0, y'(0) = 0. Plot the component curves and the orbit, the latter for the rectangle |y|< 0.25 and |y'|< 1. Any surprises? 28. Hearts and Eyes: Find a solution formula for y'' + 25y = sin&(wt), where w is not equal 5. Plot the solution curve of the IVP with y(0) = y'(0), where w=4. Plot t

Eulerian and Non-Eulerian Graphs

Let G be a connected graph that is not Eulerian. Prove that it is possible to add a single vertex to G together with some edges from this new vertex to some old vertices so that the new graph is Eulerian. Please see attachment for background and hints.

Graphs : Eulerian Trails

1. We noticed that a graph with more than two vertices of odd degree cannot have an Eulerian trail... (please see the attached file).

Graphs : Connectedness, Vertices and Edges

11. Let G be a graph with n>= 2 vertices. a) Prove that if G has at least (n-1) + 1 edges the G is connected. ( 2 ) b) Show that the result in (a) is best possible; that is, for each n>= 2, prove there is a graph with (n- 1)