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# Basic Algebra

### Distance Between Ships

At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 19 knots. How fast is the distance between the ships changing at 4 PM, in knots? (1 knot is a speed of 1 nautical mile per hour) - The final result is not around 25 (i.e. 25.XX is not correct). Please check

### Logarithms : Express as a product: log7 4&#8730;[y]

Express as a product: log7 4&#8730;[y]

### Simplifying Logarithms to Different Bases and Exponents (7 Problems)

Please see the attached file for the fully formatted problems.

### An open box with a square base...

An open box with a square base is required to have a volume of 27 cubic feet. Express the amount A of material that is needed to make such a box as a function of the length x of a side of the square base. I have A(27/x^2) +x^3....i have no clue to if this is correct.

### Algebra Word Problem : How many days before 17th August is it, if 50 days ago, it was four times as many days since March 30th?

How many days before 17th August is it, if 50 days ago, it was four times as many days since March 30th?

### Differentiation : Find Local Extrema of a Function on an Interval

Locate the absolute extrema of the function on the closed interval. f(x) = -x^2 + 3x [0,3] [Answer is minimum at (0,0) and (3,0) and max at (3/2), 9/4) Locate the absolute extrema of the function on the closed interval. g(t) = t^2/t^+ 3 [-1,1] Answer Min (0,0) Max (-1, 1/4) (1, 1/4) Locate the absolute extre

### Logarithmic Equations, Inverse Proportion 'Together and Alone'

1. If log3 12 = log4 x, then x = 2. If 6e^(n/3) = 5, then what is the value of n? 3. What is the definition of inversely proportion? I understand that in directly proportional problems you can set a ratio: x:12 = 34:32, but for inversely proportional what do I have to do? 4. Jules can make m muffins in s minutes. Alice can m

### Pressure Distribution, Bernoulli's Theorem and Flow Patterns

Consider the flow past a circular cylinder... Plot the pressure coefficient Cp along the surface of the cylinder versus &#952; for O&#8804;&#952;&#8804; pi i What is the value of Cp at &#952;=5O° ii At what point around the cylinder's surface will the static pressure equal the freestream pressure. iii If one combines a so

### Six Algebra Word Problems : Ratio and Proportion, Length of Time Together and Alone, Length of Diagonal and Period of Swing

50. Foxes and rabbits. The ratio of foxes to rabbits in the Deerfield Forest Preserve is 2 to 9. If there are 35 fewer foxes than rabbits, then how many of each are there? Page 379 Problem 40, 42 40. Envelope stuffing. Every week, Linda must stuff 100 envelopes. She can do the job by herself in 6 hours. If Laura helps

### Metric, Measure and Polynomial

If , show that there is a measure on [0,1] such that for every polynomial of degree at most , .

### Metric System Conversions

I need to be able to convert between kilo, centi, milli, micro. Can you please give me examples and explanations I get some problems right but some I get wrong. For example my teacher had this problem 5.5 kg = 5500000000 mcg Can you explain this problem also.

### Carmichael Numbers Composite Integers

An odd composite number is called a Carmichael number if a^(n-1) ≡ 1 (mod n) for all integers a with (a, n) = 1. Show that 1729 = 7 x 13 x 19 is a Carmichael number.

### Number Theory. 400 level. Introductory Course in Undergraduate.

Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields. (See attached file for full problem description)

### Number Theory. 400 level. Introductory Course in Undergraduate.

Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields. (See attached file for full problem description)

### Critical points and relative extrema

Find all critical points and determine the relative extrema of f(x,y)=1/3x3-x+xy2. (See attached file for full problem description)

### Setting up an equation and an inequality

Suppose wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and 0.5 pound of sugar. To bake each muffin, the baker need needs 0.4 pound of wheat and 0.16

### Graphing and word problems

Problem 19 Find the correct graph. Problem 20 Problem 29 Problem 30 Problem 42 Problem 47 Different interest rates. Mrs. Brighton invested \$30,000 and received a total of 2,300 in interested. If she invested part of the money at 10% and the remainder at 5%, then how much did she invest at each rate?

### Proofs: Algebra of Composition of Functions

3. This problem is about the algebra of composition of functions: a) Let f: A--> B, g: B --> C, and h: C --> D be functions. Show that (hog)of = ho(gof). b) Let f: A -->B be a function. Show that I(subscript B)of = f = foI(subscript A) c) Let A = {a, b} be a set with two elements. Find functions f, g: A--> A such that f

### Proof by Induction : Cartesian Products and Finite Sets

Please see the attached file for the fully formatted problems.

### Continuity of Functions Solved

Let f(x,y)=xy log(xy) if xy > 0, and define f(x,y) = 0 if xy = 0. Where, if at all, is f discontinuous? Please see the attached file for the fully formatted problem.

### Cartesian Product and Finite Sets and Algebra of Composition

I'd like to know the deductive techniques to prove each. A short and correct proof for each is all that is required. OR please provide some help on how to solve them. Please see the attached file for the fully formatted problems.

### Quadratic Equation Word Problem : Maximum Area

1500 feet of chain link is to be used to construct 6 animal cages as shown below. Find the maximum value of this area and the dimensions that yield this area. The area is a rectangle were the side is x. The bottom is y. It is divided by dotted lines into 6 squares where the bottom and sides are x.

### Quadratic Equation Word Problem : Maximizing Area of a Rectangle

A field is to be marked off in the shape of a rectangle, with one side formed by a straight river. If 100 feet is available for fencing, find the dimensions of the rectangle of maximum possible area.

### Lines Given Point and Slope and Writing in Standard Form

(See attached file for full problem description with symbols and equations) --- Find the slope of the line that goes thru each pair of points Draw line through with slope 1 and line through with slope 1 Draw L through and . What is the slope of any line perpendicular to . Draw through the origin so t

### Quadratic Equation Word Problem : A rectangle is 8 feet long and 6 feet wide. If each side is increased by the same amount the area of the new rectangle is 72 square feet more than the area of the or

A rectangle is 8 feet long and 6 feet wide. If each side is increased by the same amount the area of the new rectangle is 72 square feet more than the area of the original rectangle. Find the length and the width of the new rectangle.

A rectangle is 3 times as long as it is wide. If the width is increased by 6 feet and the length is decreased by 3 feet the area is doubled. Find the dimensions of the original rectangle.

### Require assistance with homework

(a) How many check bits are needed if the Hamming error correction code is used to detect single bit error in a 5602-bit data word? Show procedures to support your answer. (b) In a system bus, data lines, address lines, and control lines are separated. Why? (c) How many base-3 digits does it take to obtain as many combi

### Writing Equations from Word Problems and Inequalities

Page 211 & 212 Write a formula that describes the function for each of the following. # 8 A developer price condominiums in Florida at \$ 20,000 plus \$ 40 per square foot of Living area. Express the cost C as a function of the number of square feet of living area S. # 10 With a GM Master card 5 % of the amount char

### Questions on Polynomials, slope, finding the equation of the line

1. Find slope given the following points: (-1,-3) and (3,5) 2. Which quadrant are the following points located in: a. (-3,4) b. (2,-5) 3. Given the point (0,-3) and slope 2, find the equation of the line. Given the points (2,-5) and (-1, 4), find the following: 4. Slope and Y-intercept 5. Equation

### Finding the slope, and y-interecpt given an equation of the line Derving a function from the given data Writing Inequalities as complete sentences

Find the slope and y-intercept for each line that has a slope and y-intercept # 25 x + y = 5 # 47 x 3y #55 3 -- = --- y = --x --2 2 5 4 W