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Simultaneous Equations

Please see the attached file for the fully formatted problems. Problem 1 Solve the following equation to find x in terms of s and g in its simplest form. (Assuming that ) Problem 2 Solve the equation below for x

Word Problem

If Bob had $150 more saved he would have five times as much saved as he currently has saved. How much does Bob currently have saved?

Quadratic Residues

Please see the attached file for the fully formatted problems. Fix a positive integer a We say that a is a quadratic residue modulo n if there exists x such that a = x^2 mod n. (a) Let n be an odd prime and a be a non-zero quadratic residue modulo n. Show that there are exactly two values in{O.1....,n?1} satisfying x^2=amodn

Multipath Object Determination : Reflective Object

Find the deterministic solution for defining the position of a reflective object where the direct path and reflective path are known and the angle between the object and the receiver are also known. Please see the attached file for the diagram.

Euler Method : Solve Analytically

I have a differential equation with the initial condition given by: dy/dx=y^2/x+1, where y(0)= 1 (see attached file for more detail). As requested by my question, I have used the simple and improved euler methods to estimate y(1.2) with a step size of h=0.3 to 4 decimal places. I am struggling to solve the differential eq

Uniform Motion

Two mountain bikers started from the ranger station in Rocky Mountain National Park traveling in the same direction on Trail Ridge Road. The first biker left 1 hour earlier than the second and traveled 10 miles/hour. The second biker left later and traveled 15 miles/hour. By 4:00 pm, the second biker had passed the first and was

Time Series, Forecasting, Autocovariance and Autocorrelation

I would appreciate it if someone could provide the solution to QA1 of the attatched exam paper. SECTION A A1 (a) Give the definitions of the autocovariance and autocorrelation of a time series model. (b) Calculate the autocovariance and autocorrelation function for the time series Y = 3 + Zt + 1/2Zt-1 + 1/5Zt-2, where

Sequence of Events

Please see the attached file for the fully formatted problems. Problem 9. Let.... be a sequence of events. ... ..... and the sequence (C) is increasing..... The sets B and C are denoted by lim sup n->infinity An and lim inf n->infinity An, respectively. (a) Show that B and C are events. (b) Show that... (c) Find .... (Th

Determine the Eigenvalues of a Function

K is a field, V is the vector space of all polynomials over K, D is the derivative function from V to V and g is a linear function from V to V given by g(f(x)) = xDf(x). Find all eigenvalues of g. When are there infinitely many eigenvalues? Please explain in detail. PLEASE NOTE: it states that g is a linear functio

Standard form

Q1 Make the symbol indicated in brackets the subject of each formula shown express each in its simplest form. A. a+b+c-d-e [d] B. x=3y-t [y] C. c=2pi.r [r] D. f=9over5c+32 [c] E t=2pi square root l over g [l] q2. A formula used to calculate the power gain in an electronic amplifier in db is gain [g]=10log p2 over p1 wher


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?

Word Problem

A man's age at death was 1/29 of the year of his birth. How old was he in 1949? Hint: people rarely live past 100.

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.

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.

Word Problem

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.

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?

Quadratic equation

4.76x^2 + 6.12x = -55.3 Find all real solutions, however i am getting a negative number, which is not workable?