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 cons
Find the following. (Questions held on attachment) Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of x^3yz^4 in the expansion of c) The coefficient of x^3 in the expansion of d) The coefficient of x^5 in the expansion of is equal to the coefficient of x^4 in the
Prove by induction where n is a positive integer. (The questions are attached).
Solve this equation: 3x²- 5x -1 = 0.
Please see the attached file for full problem description.
Find the value of x: log_3 7.2 = x
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 passing through (1,-3) and parallel to x+y=2.
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.
Application of Mathematical Induction It is an application of Mathematical Induction in proving the relations of Fibonacci Numbers. To prove: F 2n+1 - Fn Fn+2 = (-1) n for n > or, = 3.
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
Simplify the following algebraic expression: 3X - (2 - X). Could you please explain the steps that I take when simplifying algebraic expressions such as this one? Thanks.
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.
Karley is twice as old as Lana. Three years from now, the sum of their ages will be 42. How old is Karley?
1. Dan's father is 45. He is 15 years older than twice Dan's age. How old is Dan?
Prove the well-ordering Axiom by strong induction.
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.
A mapping %:A->B is called a constant map if there exists b.(b not) belonging to B such that %(a) = b. for all a belonging to A. Show that a mapping %:A->B is constant if and only if %$=% for all $:A->A