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# Graphs and Functions

### GMAT practice questions Math Problem Solving

Could you please provide me with 10 or 15 practice questions for an upcoming GMAT test that focus on the Problem Solving portion of the exam?

### Parametric Equations : Find the vertex, focus , directrix of the parabola and sketch its graph AND Sketch the curve by using parametric equations to plot points.

1.) Find the vertex, focus , directrix of the parabola and sketch its graph y+ 12x - 2x^2 = 16 2.) Sketch the curve by using parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases x= 2 cos t, y= t- cos t, (0 (</=) t (</=) 2 pi)

### Unity feed-back control system with feedforward transfer function

Consider a unity feed-back control system with the following feedforward transfer function: G(s) = K(s^2+25)s/s^4+404s^2+1600 Plot the root locus (or root loci) for the system with MATLAB. Show that the system is stable for all values of K>0. Problem is also in the attached file.

### Open-Loop Transfer Function of a Unity Feed-back Control System

The open loop transfer function of a unity feedback control system is given: G(s) = K/s(s+3)^2 Sketch the root locus of the system. See attached file for the problem as well.

### Ellipses, Hyperbolas and Parabolas : Vertices, Foci, Polar and Parametric Form and Eccentricity

1.Determine the vertices and foci of the graph of x^2 y^2 ---- - ---- = 1. 16 35 As an example. Answer should look like (0, +-4/9) Veertices

### Cost, Revenue and Profit Functions and Break-Even Points

See the attached file. 3. Antonio would like to invest \$5,000. He has the choice of two accounts, one that pays 2.3% compounded continuously or the other that pays 2.5% compounded quarterly. Which account would yield the higher return? 4. A manufacturer of tennis shoes is planning a new line of shoes. For the first year, the

### Unity Feedback System and Closed-Loop Transfer Function

Determine: a) the values of K and k of the closed-loop system shown in Fig. 1 (see attached file) so that the maximum overshoot in unit-step response is 25% and peak time is 2 sec., assume that J=1 kg-m^2 . Consider a unity-feedback control system with the closed loop transfer function. b) whether system is stable or not.

### Inequalities Word Problem : Revenue Function and Graphing

A small gift shop is trying to determine the number of gift items it can sell to maintain a monthly revenue greater than \$10,000. The revenue function for this business is R = -0.10N2 +70N, where R=monthly revenue and N=number of gift items sold per month. (Total: 4 pts) a. Write the inequality for what this business is

### Data table and graph for function with 4 parts

A specialty-freezer company has determined that the operating costs at one of its plants can be approximated by the function: C = 0.35N2 - 20N + 2000 where C = daily operating cost (dollars) and N = daily production (freezers). a. Create a data table and graph of this function between N=0 and N=100 freezers. Use a

### Writing Equations and Functions from Word Problems

You are managing a small assembly operation building toy cars. Due to increased demand, you need to hire an employee in addition to the two that are already building this line of toy assemblies. For the questions below, show all your work in deriving the answer (Total: 4 pts). a. Write a function for the time, T,

### Graphing, Trends and Forecasting : Heart Disease and Cancer

The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. Year Disease 1985 1990 1995 2002 Heart Disease 771169 720058 737563 696,947 Cancer 461563 5

### Parabolas : Put the function in the form y = a(x - h)2 + k and find the line of symmetry. y = x2 - 6x + 8,

For the function y = x2 - 6x + 8, perform the following tasks: a)Put the function in the form y = a(x - h)2 + k. b)What is the line of symmetry?

### Graphing, Trends and Forecasting : Heart Disease and Cancer

You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: 1. The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. 1. Year

### Applications of Graphs and Functions: Cost Functions and Graphs

See the attached file. 11. A cable TV company charges a fee of \$28.95 per month for basic service which allows the subscriber to get local channels. A fee of \$5.95 per month is added to upgrade to premium service which allows the subscriber to receive a group of 65 channels. Subscribers with premium service are then charged \$3

### Closed-Loop Transfer and Open-Loop Transfer Functions

Consider a unity-feedback control system with the closed loop transfer function: C(s)/R(s) = Ks+b/s^2+as+b Determine the open loop transfer function G(s). Show that the steady-state error in the unit-ramp response is given by: e_ss = 1/K_v = a-K/b See attached file for equations in equation editor. Please use Micros

### Quadratic Equations : Solving, Graphing and Applications

1) Using the quadratic equation x2 - 3x + 2 = 0, perform the following tasks: a) Solve by factoring. Answer: Show work in this space. b) Solve by completing the square. Show work in this space. c) Solve by using the quadratic formula. Show work in this space. 2) For the function y = x2 - 6x

### Graphs : Solution set

(See attached file for full problem description) --- ? Identify the document by typing your full name and section number next to the yellow text. ? Rename the file by adding your last name to current file name (e.g., "u1ip_lastname.doc"). ? Type your answers next to the yellow text. ? To show your work, you will need t

### Algebra_Graphs and Functions

(See attached file for full problem description) Questions are on graphs and functions. Eight different questions are answered. Most of them involve writing functions in slope intercept form. I have answered the following questions with great detail. Please see the attached pdf file for the question description. 2, 6, 1

### What can the line graph, a parabola graph, a hyperbola and an exponential graph be used for.

What can the line graph, a parabola graph, a hyperbola and an exponential graph be used for. In real life applications. Example: A line graph can be used for instrument calibration

### Forming Functions from verbal descriptions

A power Station and a factory are on opposite sides of a river 60m wide. A cable must be run from the power station to the factory. it costs \$25 per meter to run a cable in the river and \$20 per meter on land. a. express the total cost C as a function of x the distance downstream from the power station to the point where the

### Graph Problem with Depth First Search and Breadth First Search

Let G = (V, E) be a connected and undirected graph, and u is a chosen vertex in V. Suppose starting from u, exactly the same tree T is obtained using either breadth first search or depth first search. Prove that G = T, where T is the BFS or DFS tree.

### Transfer Function

Simplify the block diagram diagrams shown in Fig. 1 and Fig.2 (see attached file) and obtain the transfer function C(s)/ R(s). Please show steps. Thanks.

### Transfer Function from Voltage, Inductance, Resistance and Capacitance

A battery of voltage Vi is connected in series with a resistor of resistance R, an inductor of inductance L and a capacitor of capacitance C. If the output voltage across capacitor is Vo, derive the transfer function.

### Applications of Logarithmic Equations

The viscosity of a liquid is a measure of its resistance to flow. Its value can be found experimentally by putting a quantity of liquid between two moving parallel plates and measuring the friction force on one plate. In such an experiment, values of the coefficient of viscosity of a lubricating oil were found at different tempe

### Graphing Compound Interest

I know that for a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, A=P(1+r/n)^m, let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4. Can you show me how you got the coordinates and how to graph

### Value of x using a graph

An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. When this is graphed for the function V that represents the volume of x, on the graph what is the function of

### Find the function for volume of an open-top box.

If I have an open-top box that is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. How do I find the function V that represents the volume of the box in terms of x? How do you

### Statistical Information

You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002.

### Graphing functions

How do I graph the functions y=x and y=the sq root of x on the same graph (by plotting points if necessary). How would I show the points of intersection of these two graphs? How would the graph relate to solving all the values of x for the equation x-the sq root of x=0?

### Algebra Functions and Graphs

It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. Year Disease 1985 1990 1995 2002 Heart Disease 771169 720058 737563 696,947 Cancer 461563 505322 538445 557,271 Plot this data