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# Basic Algebra

20. The hypotenuse of a right triangle is 22m long. The length of one leg is 0m less than the other. Find the lengths of the legs. 26. A turbo-jet flies 50 mph faster than a super-prop plane. If a turbo-jet goes 2000 mi in 3 hr less time than it takes the super-prop to go 2800 mi, find the speed of each plane Quadrati

### Torus surface area

See attached file for full problem description. A torus of radius 10 (and cross cross-sectional radius 1) can be represented parametrically by the function r: where D is the rectangle given by 0 <= theta <=2pi,

### Factor the polynomial/Express the polynomial, Simplify the expression & Evalute I don't Understand how to come up with the answer

Express the polynomial: (x2-xy) (2x+6y), (_____) 2x Factor the polynomial: x2-5, x2-7x+6, 3x2+4x+1 Evaluate: l-30lxl 1 1 __ -__ l 5 3 Simplify the

### Algebra problems

Simplify the expressions:( 54b4 x4 1/3) ( ___________), (6ax4)2 (2x)-2, 5y 4b 16bx2 ___ + ____ axy2 b

### Basic Algebra : Graphing

3) x -2 -1 0 1 2 y .25 .5 1 2 4 Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. Graph Graph Type Explanation D

### Quadratic Equations and Functions (10 Problems)

4. 2 Solve 36x + 49 = 0 2 b. Find the x-intercepts of f(x) = 36x + 49. Solve. Give the exact solution and approximate solutions to three decimal places, when appropriate. 2 6. 3x - 7 = 0 2 16. (t-2) = 25

### Radical Expressions, Equations and Functions

Please see the attached file for the fully formatted problems. Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. 14 9 23 20. so it should like this p q r I just didn't know how to d

Radical Expressions. See attached file for full problem description.

### Derive an Expression for the Closed Loop Transfer Function

Derive an expression for the closed loop transfer function: h(s) = Y(s) ---- R(s) for a gain k = 10. Work i have done so far: Ea(s) = R(s) - B(s) = R(s) - H(s)Y(s) Because the output is related to the actuating signal by G(s), we have Y(s) = G(s) Ea(s) Therefore: Y(s) = G(

### Irreducible Palindromic Polynomials, Reducible and Irreducible

3.- a) Determine the number of polynomials f(x) of degree 6 over for which f(1)=1 and f(0)=1. b) Determine the number of polynomials of degree 6 over that are reducible but have no linear factors. How this is possible, please can you explain this? Hint Consider the possible factorizations. c) Determine

### Logarithmic Equations Word Problems and Loudness of Sound

The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear. Using the Library, web resources, and other course material, research how sound is measured. Include the following items in your posting: The formula for meas

### Discrete mathamatics proofs: induction, inclusion/exclusion principle, Pascal's formula

1. Please prove the following using induction. n choose 0 = n choose n = 1 for all n greater or equal to 0 n choose k = n - 1 choose k - 1 plus n - 1 choose k for all 0 < k < n; n greater than or equal to 0 2. Please prove using the Inclusion and Exclusion Principle. Patrons of a local bookstore can sign up fo

### Algebra

Solve and graph 52. [8x - 3(3x + 2)] - 5 > = 3(x + 4) - 2x Solve: 25. Elaine's height is 67in. Determine, in terms of an inequality, those weights W that will keep her body mass index below 25. 76. A long-distance telephone call using Down East Calling costs 10 cents for the first minute and 8 cents for each additional

### Work done in moving a rock.

A rock with a mass of 1 kilograms is put aboard an airplane in New York City and flown to Boston. How much work does the gravitational field of the earth do on the rock? I think the gravitational field G needs to be factored in.

### Determine in terms of an inequalities

Inequality Calculations. See attached file for full problem description. 9.1 52. [8x - 3(3x + 2)] - 5 ≥ 3(x + 4) - 2x First distribute it into the parenthesis, then move x into the left side of the inequality. Remember to change the sign if a negative number is multiplied or divided. 72. Elaine's height is 67 in.

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.

### Prioritize these jobs by SPT (shortest processing time), EDD (Earliest Due Date), FCFS (First Come First Serve) and Slack (Promised Time - Processing Time).

Alice's Alterations has eight jobs to be completed and only one sewing machine (and one sewing machine operator). The following jobs are waiting to be scheduled for the sewing machine. The letter of the alphabet indicates the sequence in which the jobs arrived. It is now the beginning of Day 5. Job Processing Time (in da

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx +

### L'Hopital's Rule, Infinite and Zero Powers and Limits

Many students incorrectly evaluate the indeterminate forms of type 0^0 , type &#8734;^0 , and type 1^&#8734; as 1 because they think that "anything to the zero power is 1" and "1 to any power is 1." These rules are indeed true for powers of numbers. But 00 , &#8734;0 , and 1&#8734; are not powers of numbers but descriptions of l

### Examples of graphs: line, parabola, hyperbola, exponential

Using the Library, web resources, and other course materials, find a real-life application of each graph. Relate the application to the specific graph (line, parabola, hyperbola, exponential). Describe the characteristics of each application as related to the graph.

### Network Diagram Depicting the Various Activities in the Project

Recently, you were assigned to manage a project for your company. You have constructed a network diagram depicting the various activities in the project (figure 3.15). In addition, you have asked your team to estimate the amount of time that they would expect their activities to take. Their responses are shown in the following t

### Power Series : Convergence and Divergence

1. Suppose that converges when x= -4 and diverges when x = 6. What can be said about the convergence or divergence of the following series? 2. Suppose that the power series 3. Suppose that the series Please see the attached file for the fully formatted problems.

### Evaluating Functions and Describing Function Change Rates

Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. f(x) = 3x + 2 f(x) = x2 + 5x + 6 f(x) = x3 + 3x2 + 2x + 1 f(x) = ex f(x) = log x

### R-Modules and Submodules

(10)Let R be a ring with 1 and let M be a left R-module. Let N be a submodule of M. Prove that if both M/N and N are finitely generated then so is M.

### Common and Natural Logarithms

Common and Natural Logarithms 1. For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled. The exponential function f (x) = e^x you will also need to graph f (x) = e^(2x). The common logarithmic function f (x) = log x You will also need to graph f (x) = log (2x).

### Bouncing ball Lab - Algebra

Lee Way was conducting an experiment with a new mega ball. Use the following tables of values to complete the question for Part I (A) Identify the independent variable and the dependent variable. x=_________________ y=_____________ (B) Graph your results (C) What is the rebounding height if the ball is dropped from 10

### Graphs of Exponential and Logarithmic Functions

Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer. y = 2x y = log2x See attached file for full problem description.

### Develop separate schedules by using the FCFS, SPT and EDD rules. Compare the schedules on the basis of average flow time,the average early time and average past due hours for any order.

The hickory company manufactures wooden desks. Management schedules overtime every weekend to reduce the backlog on the most popular models. The automatic routing machine is used to cut certain types of edges on the desktops the following orders need to be scheduled for the routing machine: Order Estimated Machine time(h

### Equations and graphing

See attached file for full problem description. 1. Rewrite the equation 4x - 10y = 11 as a function of x. 2. Write the equation of the line that passes through point (1, -8) with a slope of 0. 3. Given f(x) = 5x2 - 3x + 1, find f(-2). 4. Write the equation of the line passing through (-6, -3) and (-6, 1). 5. One day,

### Quadratic Equations Word Problems : Open Top Box

Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?