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Algebra

Difference in Area

A lot of 40 meters by 36 meters. A house 27 meters by 9 meters is built on the lot. How much area is left over for a lawn?

Logarithims and Exponents

If the amplitude ratio, N in decibels, of an electrical system is given by the formula;- N=10log(Po [output]/Pi [input]) and the power is given by;- P=V^2/R Show that for matched input and output resistances the output voltage V[output] is related to V[input] by ;- Vo[output]=Vi [input] 10^(N/20) If N is increa

Solving Equations

1. 2x^1/4 = 9 - 4x^-1/4. Answer given 1/16 and 256. 2. 6x^1/3 + 5 + x^-1/3 = 0. Answer given -1/27 and -1/8 3. x^3 + 8 = 9x^3/2. Answer given 1 and 4 4. 27^x = 9. Answer given 2/3 5. 8^x = 4^1-x. Answer given 2/5

Indices

From a textbook- Solve the following equations for x: 1. 7x^1/2 + 2 = 0. Answer given 4/49 2. 6x^3/2 - 2/3x^-1/2 = 0. Answer given 1/3 3. 5x^3/4 + 40 = 0. Answer given 16 Any help appreciated - I'm struggling wit this particular type of equation

Writing Inequalities from Word Problems

Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2500? Write an inequality that illustrat

Linear Programming

Consider the following linear programming problem. MIN Z = 10x1 + 20x2 Subject to: x1 + x2 >= 12 2x1 + 5x2 >= 40 x1, x2 >= 0 What is minimum cost Z=?? Put your answer in the xxx.x (to one decimal place)

Graphing Asympotes

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. Prove Algebraically. See attached file for full problem description.

Prove that W is a Subspace of V

Let F be the field of real numbers and let V be the set of all sequences: (a_1, a_2, ..., a_n, ...), a_i belongs to F, where equality, addition and scalar multiplication are defined component wise. Then V is a vector space over F. Let W = {(a_1, a_2, ..., a_n, ...) belongs to V | lim n -> infinity a_n = 0}. Prove t

Arithmetic and Geometric Series and Sequences

Using the index "n" of the partial sums of a series as the domain, and the value of the corresponding partial sums of the series "Sn" as the range, is a series a function? Please include in your answer: - Which of the basic functions, (i.e. - linear, quadratic, rational, exponential), is related to the arithmetic series? -

Solving equations, difference between relation and function

Please see the attached file for full description Find all real or imaginary solutions to each equation: 98. X - 1 = 2x - 3 X + 2 x + 4 Find exact and approximate solutions to each problem 106. One on one. Find two positive real numbers that differ by 1 and have a product of 1. 115. Decathlon champion. For

Writing Equations from Word Problems

12) You have exactly $537 to spend on parting gifts for your rich uncle's birthday party. You decide to get watches for the ladies (at $27.98 each), and beepers for the men (at $23.46 each). You know that the number of watches required will be 3 times as much as the number of beepers. How many of each item do you buy?

Linear Relationships, Slope and Intercept

1. The following data shows the relationship between the total average amount of student study time in an Online course and their corresponding average grades. Hours Studied 50 57 69 112 120 88 96 Grade 60 63.5 69.5 91 95 79 83 Is this relationship linear? Explain why or why not 2. Line 1 passes through the points

Solution Sets and Interval Notation

Please see the attached file for the fully formatted problems. 4. Solve |4x - 7| > 11 and write set notation for the solution set. A. B. C. D. 5. For f(x) = x4 - x3 - 5, use the Intermediate Value Theorem to determine which interval contains a zero of f. A. Between 1 and 2 B. Between 2 and 3 C. B

Solution Sets and Interval Notation

1. Consider the quadratic function f(x) = - x2 + 8x - 10. Determine whether there is a maximum or minimum value and find that value. A. Minimum is - 6 B. Minimum is - 26 C. Maximum is - 26 D. Maximum is 6 2. Solve |9 - 2x| < 5 and write interval notation for the solution set. A. (2, 7) B. (- 7, -2) C. (–∞,

Solving Equations

Please solve x: 1.8 x 10^-5 = [10^-5] * x/3.0-x Solve: 0.1 Kf = ----------------- y * (3 - x)^4

Family of ideals in a ring

Show that the intersection of any family of ideals in a ring is an ideal. Show that the ideal generated by a subset S of a ring R is the intersection of all ideals J of R such that S <= J <=R.

How many birds are needed to decorate the table?

Caitlin is decorating a rectangular table . She wants to decorate the table with paper cutouts birds. She plans to tape a bird every 6 inches around the table and at every corner . The table is 2 feet wide and 5 feet long; How many birds are needed to decorate the table?

Finance/Accounting Problem1. Compute the present value of a $100 cash flow for the following combinations of discount rates and times: 2. Compute the future value of a $100 cash flow for the following combinations of discount rates and times:

1. Present Values. Compute the present value of a $100 cash flow for the following combinations of discount rates and times: 1. r = 8 percent. t = 10 years. 2. r = 8 percent. t = 20 years. 3. r = 4percent. t = 10 years. 4. r = 4 percent. t = 20 years. 2. Future Values. Compute the future value of a $100 cash flow fo

In this problem, a pyramid having rectangular base has a base length of 180 yards and width 62 yards. It has a height of 100 yeards. If the density per cubic yard is given to be 432 lb per cubic yard, we have to find the weight of the pyramid. For complete description of the question, please see the long description of the question.

A new pyramid has been found in South America. The pyramid has a rectangular base that measures 62 yd by 180 yd, and has a height of 100 yd. The pyramid is not hollow like the Egyptian pyramids and is composed of layer after layer of cut stone. The stone weighs 432 lb per cubic yard. How many pounds does the pyramid weigh?

Volume of a Hemisphere Word Problem

A dentist places a gold filling in the shape of a cylinder with a hemispherical top in a patient's tooth. The radius of the filling is 3 mm. The height of the cylindrical portion is 4 mm. If dental gold costs $16.00 per cubic millimeter, how much did the gold for the filling cost? Round to the nearest cent. Use pi &#8776; 3.14.

Variables, Term and Powers

--Is there a difference between -7^2 and (-7)^2 --Consider a number without any variables, say, 10. Is 10 a term?