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Exponential Growth Word Problems

A colony of 1000 bacteria is introduced to a growth-inhibiting environment and grows according to the formula n = 1000 + 50t + t^2 How many bacteria are present after 3 hours?

Solving Equations

Solve for t. Where t is a real number. Divide with commas, if there is more than one solution. principle square root t + 19=4

Substitution of "v" in a 2nd order d.e.

I have been tasked with solving y'' - 3y^2 =0 using the technique used substituting v for y', therefore substituting v dv/dy for y''. (Equation with "x" missing) I broke it down as follows Y'' -3y^2 =0 Y'' =3y^2 Substituting I get v dv/dy = 3y^2 Separating variables, I get v dv =3y^2dy Integrating I get 1/2v^2 +c = y^3 +c

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.

Limits Word Problems

A wholesaler prices the best latex flat paint at _15x_ x - 1 dollars per gallon where x is the number of gallons ( x > 1). The more you buy, the lower the price will be per gallon. As you buy more and more gallons, what price per gallon does the paint approach?

Solving Equations

Solve the following equation for x . Write the answer as a fraction in simplest form. -7 (x-8) = 5x + 3 + 5 (-6x + 4)

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 differenc

Order of Operations

Explain how subtracting [4w/(w^2-8w+150]-[6/w-3)] is similar and different to substracting 4/5 - 2/15. Show all steps in both addition problems.

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.

Exponential function application

Attached are the questions 1. Complete table for savings in which interest is compounded continously. 2. Complete table for radioactive isotope 3. The population of P of a city is given by P= 105300 e^0.015t, where t represents the year with t=0 corresponding to 2000. Sketch the graph of this equation. According to this

Groups: Conjugacy Classes

2.99 (iii) Show that there are two conjugacy classes of 5-cycles in A5, each of which has 12 elements.

Quadratic congruences

8. Find all solutions to the quadratic congruences, if they exist. (a) x2 + x + 1 ≡ 0 (mod 7). (b) x2 ≡ 55 (mod 179)

Quadratic residue

Classify every integer a, 1<=a<11 as to whether it is a quadratic residue or nonresidue modulo 11.

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