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Algebra

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.

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

Determining Sample Size: Example Questions

1) Solve formula for variable: The formula for the margin of error to establish a confidence interval has been found mathematically to be: e= z s / square root of n Where: e = margin of error z = critical value s = sample standard deviation n = sample size Giv

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

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

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

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

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..

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}

Surface area of a right circular cylinder

The surface area of a right circular cylinder is given by the formula S= 2*PIE SIGN*rh + 2*PIE SIGN* r^2, where r is the radius of the base, and h is the height of the cylinder. Solve the formula S= 2*PI*rh + 2*PI*r^2 for h.

Complex Theorem for Continuous Anti-Derivative

Although Corollary 2 does not apply to the function 1 / (z — z_0) in the plane punctured at z_0, Theorem 6 can be used as follows to show that (see attached 1) for any circle C traversed once in the positive direction surrounding the point z_0. Introduce a horizontal branch cut from z_0 to infinity as in Fig. 4.25. In the r

Linear programming investment problem

Below problem is one that I'm drawing a blank on for even setting up the equation. Any help would be greatly appreciated. Smith recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a st

Company's Payroll

A new computer can process a company's monthly payroll in 1 hour less time than the old computer. To really save time, the manager used both computer's and finished the payroll in 3 hours. How long would it take the new computer to do the payroll itself? Question also in attachment.

Solving Equations and Square Property

Can you please see if I'am doing these equations correctly? And if I am not, then can you please explain in detail where I went wrong? Please see the attached file for the fully formatted problems.

Square Root Symbols in a Function

Here's the formula... The answer should be 4, which should be W S=10 T=5 w=4 w=33-(10 - 0.28 x S + square root of 28xS ) x ( 33 - T ) / 22.727 so.. the square root symbol was over top of 28 and S just don't know how to put that symbol in here... so.. you work from left to right... and you do what's in the ( )

Distance, velocity and time relations

Florence averaged (26.2/x) miles per hour (m/hr) for the x hours(hrs) in which she ran the Boston Marathon. If she run at that same rate for ½ hours (hrs) in the Manchack Fun Run, then how many miles did she run at Manchack? Use the formula for "d" given above.

Equations for Reduced Fare Tickets

A commuter airline sells tickets for a flight at three rates: full fare, half far (for children), and early booking reduced fare (no further reduction for children). Fifty full fare, 12 half fare and 46 reduced fare tickets are sold for a total of $18,600. The reduced rate is $25 less than the half fare rate. Find the three rate