### Quadratic functions, zeros, graph

Give a simple example of a quadratic function that has no real zeros. Explain how its graph is related to the x-axis.

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Give a simple example of a quadratic function that has no real zeros. Explain how its graph is related to the x-axis.

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

Please see the attached file for the fully formatted problem. 19. Show that x = tan^-1(x) has a solution alpha. Find an interval [a,b] containing alphasuch ythat for every x E [a,b] the iteration xn+1 = 1 + tan^-1(xn) n>=0 will converge to alpha. Calculate the first few iterates and estimate the rate of convergence.

Use the given information to draw the graph on an interval near the indicated point (x = 4). If there is not enough information given, then state this fact. f(4) = 2 f ' (4) = DNE f '(x) > 0 for x > 4 f '(x) < 0 for x < 4 f " (x) < 0 for x < 4 f " (x) < 0 for x > 4

Find the point on the graph of the equation y^2 = 4x that is closest to the point (2,1).

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

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.

Please explain the basics of x,y graphs.

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)= ------------------------ ***

1. Find the domain and range of the function: f(x)=6xsquared+4 2. Find the distance between the two plotted points;(-5,2) (4,-4) 3. Using graph of f(x)=x squared as a guide, graph the function; g(x)=(x-3)squared+4 _____________________________________________________________________ 2

1. Find the slope of the line passing through the pair of points (2,-8), (2,2) Answers A.0 B.5/3 C.undefined D.5/2 2. Determine whether the graph of the equations are parallel, perpendicular, or neither -8x-7y=8 6x-2y=8 3. Find the vertex of the graph of the function; f(x)=(x+2)second power=4 A.(-2,-4)

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

Real Analysis Gradient, Divergence and Curl (I) If r = xi + yj + zk and R denote ║r║ Verify (1) ▼R^n = nR^(n-2) r

43. (3y+2) (2y^2-y+3) *44. (4y+ 3) (y^2+3y+1) 46. (m^3-4mn^2)(6m^4n^2-3m^6+m^2n^4) *90. (5-6y)(3y^2-y-7) *91. Office Space. The length of a professor's office is x feet, and the width is x+4 feet. Write a polynomial that represents the area. Find the area if x=10ft. 100. If a manufacturer charges p dollars each

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

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?

Please address the following: How do you determine horizontal asymptotes, if any, given the equation for a rational function?

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

Determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 1__ x + 4

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

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

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?

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?

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) =

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?

If function f(x) = x^2-3x-4, find and simplify f(x+h)-f(x)/h

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?

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)

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)

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).