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    Algebra

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    Forces of a log and cable

    A chain is wrapped around a log. What pull will be necessary at an angle of 52 degrees to move the log at an effective rate of 234 N along the log? A cable is wrapped around a tree creating an angle of 49 degrees. The tension on each segment of the cable is 46 N. What is the resulting force on the tree?

    6 Algebra Questions: Equations

    1.Determine the equation of the line through (-2, 0) with slope . Write the equation in standard form using only integers as the coefficients. 2.Determine the equation of the line through (0, 9) that is parallel to the line 3x + 5y = 15. Write the equation in slope-intercept form. 3.Determine the equation of the line th

    Convergence of Sequence and Proof

    See attached file for full problem description. Use the definition of convergence of a sequence to prove that the sequence (n-1)/(n+2) (n=1 to infinity) converges to 1. Please provide complete proof and explanation.

    Initial-Value Problem : Euler and Runge-Kutta Method

    Solve the following initial value problem by Euler's method using h = 0.1. Find an error by comparing to exact solution. Then solve it by the Runge-Kutta method. Find an error. dy/dx = 3xy²; y(0) = 1; 0 ≤ x ≤ 1

    Solve the Heat Equation

    7. Solve the heat equation attached. Please do #7 only. Show step by step work and explanation of the solution, please. (Answer is provided in the attachment.)

    Steady State Solution

    Please see the attached file for the fully formatted problems. Suppose that we have the heat equation with the boundary-initial data where T_0 and T_1 are positive constants. Find a steady state solution of this equation. Use this knowledge to rewrite the solution u(x,t) of the initial-boundary value problem in the form u

    Richter Scale and Severity of Earthquakes: Energy and Magnitude

    The Richter Scale provides a comparative measure of the severity of earthquakes. The original formula developed in 1935 was: R = logE, where R is the magnitude on the Richter Scale and E is the energy of the of the earthquake. (a) How much stronger than a 5.0 is an earthquake that measures 7.0 on the Richter Scale? (b) What wo

    Evaluate Functions for Given Value of X

    Evaluate the functions for th values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x (i.e. is there a pattern in the change, did the values double, or triple, increase by a certain factor, etc. 1. f(x) = 3x -2 2. f(x) =x2 - 5x +6 3. f (x) =x3

    Asymptotic Behavior of Solution

    Use the phase line to predict the asymptotic (*see attachment*) behavior of the solution satisfying the specified initial condition ... *Please see attachment for complete question.

    Symmetry: Symmetries of a Square

    Please see the attached file for the fully formatted problems. ? Let S be a square, with vertices labelled (anticlockwise), 1,2,3,4. a symmetry of S is a rotation or reflection which preserves the square (although it may change the position of the vertices). Note that a symmetry is determined by its effect on the vertices.

    Line Intersections

    Please see the attached file for the fully formatted problems. If P, Q are the midpoints of AB, CD respectively prove that i) AC + BD = 2PQ ii) AC+BC+AD+BD=4PQ ABCD is a quadrilateral. The midpoints of AB, BC, CD and DA are P,Q,R and S. Prove PQRS is a parallelogram. Find perpendicular distance from point... to line..

    Word Problem: Lengths of a Board

    A 20-foot board is cut into two pieces, Twice the length of the shorter piece is 4 ft more than the length of the longer piece. Find the length of the shorter piece.

    Calculate the Unit Conversion

    An M&M has a volume of approximately 0.5 cm3. We have Avagadro's number of M&M's. The only place to store the M&M's in in Death Valley. The area of Death Valley is approximately 100miles2. How thick in miles would the layer of M&M's be?

    Solving Equations Provided

    Please assist me by solving the attached equations. Thanks. SOLVE THE EQUATION 12. SOLVE EACH EQUATION AND WATCH FOR STRENANEOUS SOLUTIONS. 29.

    Quadratic Real Solutions

    I am supposed to find all real solutions: 1.5x^2 - 6.3x - 10.1 = 0 I am stuck, please see attachment

    Graph the equation

    Can't figure out how to solve: x^2 + y^2 + 4y = 0 I need to graph the equation in a xy coordinate system.

    Multistep word problem: Estate inheritance

    An estate valued at $62000 is left by a will as follows: to each of two grandchildren a certain sum, to the son twice as much as the two grandchildren together, and to the widow $2000 more than to the son and grandchildren together. How much goes to each?

    Supremum and Infimum of a set

    Find the Supremum (supS) and the infimum (infS) and indicate if supS is in the set S and if infS is in the set S: S = {r in N: r^2 <= 15} S = {r in Q: r^2 <= 15)} S = {[(/1)^n][(n-1)/n]: n in N} S = {x in R: x^2 + x - 1 < 0}