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

Please see the attached file for the fully formatted problems.

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Please see the attached file for the fully formatted problems.

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.

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

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

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

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

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

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)

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)

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

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?

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.

(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

(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

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

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

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

Perform the indicated operation: 1) 2) 3) 4) 5) Simplify: 6) -6x + 3x 7) (-7r)(-5r 8) 2a(a + 4) -5(3a - 2) 9) 7a - 5(a + 2) - 3 - a 10) Find the value given a = 4, b =3 and c =2: c Solve each equation 11) + 5 = 14 12) -4y = -4 + 6y 13) 14) 5y - 5(2y + 2) = 0 Solve for y: 18) 5x

28. y < 1 38. y>x, y<-x 39. x+y<5 x-y>-1 34. 3x+2y<2 -x-2y>4 25. y>2x-4 y<2x+1 16.y>2x-1 y<-x-4 17. x+y>5 x-y<3 27. y>x x>3 37. y>3x+2 y<3x+3 32. y<2 2x+3y<6

Anne decides to start a vegetable garden and buys 100m of wire netting to fence off a rectangular area from the rabbits.Assume that Anne uses an existing fence as one side of the rectangle, and the 100m netting for the other three sides. - If x is the width of the rectangular garden, write an expression for the length of the

Page 71 & 72 # 27 0.5 = -2.5 + x # 28 0.6 = - 1.2 + x #52 2 4x -- = -- 3 3 # 57 1 --y = -- -- 3 # 91 Cigarette c

Given the curve y = ax3 + bx2 + cx + d, a ≠ 0 Find the relation between the parameters a, b, and c that will ensure that the curve: (a) has only one turning point. (b) has no turning points. ---

# 23. 2 = x + 7 # 24. 3 = x + 5 # 48 2 # 49 3y --x = - 8 90 = -- 3 4 # 92. World gain demand. Freeport McMoRan projects

A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cent the price is raised, 20 fewer people go to the movies. The equation is R= -40c to the power (exponent) of 2 + 84c describes the relationship between the cost of the tickets, c dollars, and the amount of

(See attached file for full problem description with equations) --- 1. The diameter of the Milky Way disc is approximately 9  1020 meters. How long does it take light, traveling at 1016 m/year to travel across the diameter of the Milky Way? Time = distance/speed = 9  1020 m/1016 m/year = 9*104 years

Page 17 & 18 10. 7 ? -- = -- 2 8 18. 5 ? -- = --- 7 98 30. 34 102 31. 70 -- 102 40. 5 12 -- . -

(See attached file for full problem description with complete equations) --- 1. The diameter of the Milky Way disc is approximately 9  1020 meters. How long does it take light, traveling at 1016 m/year to travel across the diameter of the Milky Way? 2. Divide. 3. Multiply. Write the answer in

Algebra problems: Page 24 55. - 0.03 - 5 56. 0.7 - (-0.3) 71. - 161 - 161 72. - 19 - 88 94. Net worth. Melanie has a $ 125,000 house with a $ 78,422 mortgage. She has $ 21,236 in a savings account and has $ 9,477 in credit card debt. She owes $ 6,131 to the credit union and figures that her

Let Pn denote the assertion "n^2 + 5n + 1 is an even integer." 1. Prove that Pn+1 is true whenever Pn is true. 2. For which n is Pn actually true? What is the moral of this exercise?

See the attached file. 1. Find the axis of symmetry. y = x2 + 5x - 7 2. Solve. 5(x - 2)2 = 3 3. Solve by completing the square. x2 + 2x - 8 = 0 4. Find the x-intercepts. y = x2 + 5x + 2 5. Is the following trinomial a perfect square? Why? x2 + 18x + 81 6. The demand and supply equations for a cert