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Algebra

Solve: The Slope of a Perpendicular Line

Consider the line x+5y = 5. Please address the following questions: What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?

Solve the recurrence

Solve the recurrence T(n) = 2T(sqrt(n)) + 1 by making change of variables. The solution should be asymptotically tight. 2. Use a recursive tree to give an asymptotically tight solution to the recurrence T(n) = T(n-a) + T(a) + cn, where n > = 1 and c > 0 are constants.

Recursive Definitions

I want to get a better understanding of how these problems are done. For Exercises #1-3, decide whether the sequences described are subsequences of the Fibonacci sequence, that is, their members are some or all of the members, in the right order, of the Fibonacci sequence. 1. The sequence A(n), where A(n) = (n-1)2^n-2 +

Finding the Equation of a Line

Find the equation of each line in the form y = mx + b if possible. The line through the origin that is perpendicular to the line through (-3, 0) and (0, -3)

Solving Differential Equations

Please help solve this seperable equation and a possible suggestion on how to look for factors to multiply by in order to make it exact. (x+y)dx - xdy = 0

What is the hottest temperature reached?

The temperature inside a kiln used to bake clay pottery is given by T(x) = -0.4x^2 + 32x + 73 degrees F where x is the number of minutes the kiln is on and 0 <= x <=80. (see equation in attached file)

Solving Equations

Find all real and imaginary solutions to the equation. 49x^2 + 9 = 42x

The Stabilization Ratio (births/deaths) for South and Central America

The stabilization ratio (births/deaths) for South and Central America can be modeled by the formula y = -0.0012x^2 + 0.074x + 2.69 where y is the number of births divided by the number of deaths in the year 1950 + x a) use a graph to estimate the year in which the stabilization ratio was at its maximum. b) use the formula to

Word Problem: Distance

Anne is pulling on a 60 foot rope attached to the top of a 48 foot tree while Walter is cutting the tree at its base. How far from the base of the tree is Anne standing?

Write answer in a + bi

Perform the operation. Write answer in the form a + bi 6 + principle square root -18 --------------------------------- 3 NOTE: I'm unsure how to graph the symbol for principle square root. I hope this makes sense.

Need help with sequence of arithmetic and finite series.

(See attached file for full problem description) 1. Find the sum of the finite geometric series to three decimal places. 9 n Σ - 3(0.5) n=3 2. Write the first 5 terms of the specified sequence. Determine whether the sequence is arithmetic. If it is, find the common difference.

Finding the equation of a line.

Given a line containing the points (1,4), (2,7), and (3,10) determine the slope-intercept form of the equation, and graph the function. Give the domain and range as defined by the points, and also the domain and range of the entire function.

Problem Set

(See attached file for full problem description with proper symbols) --- 1. Given that s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56. 2. If y = x , calculate the value of p given that y = 2.65 and x = 0.745. 3. If x = (1 + 1nr), evaluate r when x =0.34, P = 1.08 and

Scatter Plot

Question 6: House cat owners invest a lot of time and expense to find just the right cat food for their finicky, spoiled and pampered pets. Some house cat owners believe that the reaction of the house cat, in terms of how much time passes between the serving of the food and the point at which the finicky, spoiled and pampered

Fundamental Theorem of Arithmetic

Please show complete solution so that I may understand the reasoning behind each step. I will need a thorough understanding to complete future assignments. See attached file for full problem description.

Exponential Growth Rates

Consider the following disaggregation of carbon emissions: Carbon emissions(kg C/yr)= Population x (Energy(kJ/yr)/Person) x (Carbon (kgC)/Energy(kJ)) Using the following estimates for the United States and assuming that growth rates remain constant, Population (kJ/yr)/Per

Word problem

In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive? (Please show steps) I'm trying to figure out what the steps would be to come to this conclusion. The problem says "220 more votes". I understand that (I think) to be +200, but

Given information in attachment, please sketch the graph

(See attached file for full problem description with proper equations) --- Given information in attachment, please sketch the graph. For the rational function f(x) = (x2 - 1) / (x2 - 9), give the intercepts and asymptotes and sketch the graph. Let f(x)=0, we get x=1 or x=-1. So, the x-intercepts: x=1 or x=-1. Let x=

Rational function

For the rational function (see attached file) a.) determine the equation of the oblique asymptote b.) determine the x-intercepts c.) determine the y-intercepts d.) determine the equation of the vertical asymptote e.) sketch the graph

A computer is infected with the Sasser virus.

A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc. How long until 100 million computers are infected?

Synthetic Division, Intermediate Value Theorem and Asymptotes

21) Use synthetic division to find: f(?2) f(x)=2x3?3x2+7x?12 21) 22) For the function f(x) = ?x3 + 8x2 ? 40 Show how to use synthetic division to find out if -1 is a zero. 22) 23) One of the zeros of the function f(x) = ? 7x2 + 17x ?15 is 2-i. Find all the other zeros. 23) ____________________ 24) Use the intermediate val