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Graphs and Functions

Linear functions, graphs, slope

As one descends into the ocean, pressure increases linearly. The pressure is 15 pounds per square inch on the surface and 30 pounds per square inch 33 feet below the surface. (A) If p is the pressure in pounds per square inch and d is the depth below the surface in feet, write an equation that expresses p in terms of d. [Hint

Depreciation: linear functions, graphs, slope

Office equipment was purchased for $20,000 and is assumed to have a scrap value of $2,000 after 10 years. If its value is depreciated linearly (for tax purposes) from $20,000 to $2,000: (A) Find the linear equation that relates value (V) in dollars to time (t) in years. (B) What would be the value of the equipment after 6 yea

Simple interest: linear functions, graphs and slopes

The simple interest formula says that if $1,000 is invested at 7.5% (r=0.075), then A=75t+1000, t>=0. (A) What will $1,000 amount to after 5 years? After 20 years? (B) Sketch a graph of A=75t+1000 for t between 0 and 20. (C) Find the slope of the graph and interpret verbally.

Graphing Functions and Descartes' Rule of Signs

1. Use Descartes` Rule of Signs to determine the possible number of positive real zeros of the function. F(x)=3x cube-4x squared-2x-4 ***************x squared +11x+28 2. Graph: f (x)= ------------------------ ***************x squared +8x+16 ****************3x squared -3x-1 3. Graph: f (x)= ------------------------ ***

Graphs : Y as a Function of X

1. Which equation defines y as a function of x? answers a. y=-3x+4 b.y=-3 c.-6x second power -3y second power=4 d.x=10 2. m=-4/5,(5,7) answers a.5x=4y=-15 b.5x=4y=55 c.4x=5y=55 d.4x=5y=-15

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).