### College Algebra

Please help me with #4, #10, and #16. I am having trouble woth these. Please show your work so that I may better understand the process.

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Please help me with #4, #10, and #16. I am having trouble woth these. Please show your work so that I may better understand the process.

Solve: x3 - 2x2+x=-5(x-1)2.

Let m be the smallest positive integer such that @^m=E for all @eS_n. Show that m=lcm(2,3,4,5,...,n). note: e denotes element of

Assume that the sum and product of two roots of a quadratic equation are 5 and 6, respectively. Find two roots.

I am asked to verify Fubini's Theorem for an integral evaluated over an equilateral triangle. I am asked to fully discuss the reasons for the limits of integration in my solution. See attached file for full problem description.

9q^2-72q+750

Test the following for divisibility by 2,3,4,5,6,8,9,and 10. (No calculator, explain your thinking). i. 6 543 210 b. What is the smallest whole number that is divisible by 2,3,4,5,6,8,9 and 10.

Simplify each of the following expressions further and identify the number property(ies) used in each. 1. 2 x (15+8)= (2 x 15)+ (2 x 8)= 2. 5/2 x (3/4 x 2/5)= (5/2 x 2/5)x 3/4=

Please see the attached file for the fully formatted problems. Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of in the expansion of c) The coefficient of in the expansion of d) The coefficient of in the expansion of is equal to the coefficient of in the

Three numbers are in arithmetic progression. The sum of the three numbers is 30 and the sum of their squares is 398. What are the three numbers? b) An arithmetic series is such that its first term is a and its third term is b. The sum of the first n terms is Sn . Find S4 in terms of a and b. Given that S4, S5 , S7 are con

Prove by induction where n is a positive integer. (The questions are attached).

Solve this equation: 3x²- 5x -1 = 0

Find a new dependent variable such that the equation becomes linear in that variable. Then solve the equation: 1/(y^2 + 1) y' + 2/x tan^-1 y =2/x

First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly: [cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0

Solve for either the general solution or relation. xy' - y = x(1 + e^(-y/x))

If the perimeter of a rectangle is 10 inches, and one side is one inch longer than the other, how long are the sides? Can you show me the steps to take to work out this and similar problems.

Diagonals in a Rectangle. In the case of a 2 X 2 rectangle, or a 3 X 5 rectangle, we can simply count. However, can we make a decision about a 100 X 167 or a 3600 X 288 rectangle? In general, given an N X K rectangle, how many grid squares are crossed by its diagonal?

Find the equation of a line L which passes through the point (1,4) and is perpendicular to the line: 6x + 3y=12.

The endpoints of the diameter of a circle are P=(-3,2) and Q=(5,-6) Find: (i) the center of the circle (ii) The radius of the circle (iii) the equation of the circle.

Logarithmic and Exponential Equations. See attached file for full problem description.

Solve for x: log2x=8 Write as a single logarithm: 5lnx-1n(x+1)

Log(x) means in this problem a log of base 3. ie, log(3)=1 sqrt(x) means the square root of x. ie, sqrt(25)=5 Solve the following equation for x: x^[log(9x)]=3sqrt(x)

Solve the integral using partial fraction decomposition. This example has a denominator that is the product of quadratics. Example 1) S (x2 + x +1)/[(x2 + 3x +1)(x2 +4x +2)] dx

2 - 13 divided by negative 76 + 15

D divided by ab(c to the 4th) plus c divided by a(b to the third) c

A 5000 gallon aquarium is maintained with a pumping system that circulates 100 gallons of water per minute through the tank. To treat a certain fish malady, a soluble antibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te-t/50 oz/gal, where t is measured in minutes. The well-

I will use the ^ sign for the squared sign. Write the following algebraic expression in its simplest form: x^ + 2x + 3x^ + 2 + 4x + 7

Can you provide me with the basic steps for solving problems in algebra? Please provide an example (e.g., a problem solving for the variable x) using these steps.

1. Dan's father is 45. He is 15 years older than twice Dan's age. How old is Dan?

Suppose that n straight lines in the plane are positioned so that no two are parallel an no three pass throught the same point. Show that they divide the plane into 1/2(n^2 + n + 2) distinct regions.