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# Algebra

### Solve the Equation

27= -9w -3k= -18 c/6= -1 y/-12 = -12 n/-5 = 11 t/6 = -10 q/-5 = 30 8n = 112 -4 = -2r

### 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

### Solve Quadratic Equation by Squaring

Please solve the attached equation by squaring. Thank you.

### 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

### U-Substitution and Integretion by Parts (6 Problems)

Please show all the steps needed to solve the attached integrals.

### 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

### Find the best constant bounds

Give examples of events to show that these bounds cannot be improved (SEE ATTACHED).

### 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

### Rearranging formulas 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

### Intersection of planes

Is it possible for three planes to intersect in a single point?

### Rational functions and y-value question

By looking at the equation for a rational function, how can you tell if there will be "y-values" which never occur?

### Find horizontal asymptotes of each rational function

Find the horizontal asymptotes of each rational function. F(x) = 4x² + 1__ x² + x + 1

### 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?

### Word Problem for a Man's Age

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

### Use definition to show that sequence is Cauchy.

Use the definition to show that the sequence (n-1)/(n+2) (n=1 to infinity) is Cauchy. Please show all steps.

### 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.

### Definition of Cauchy Sequence and Negation

State the definition of a Cauchy sequence. Also, by negating this definition, state the definition of a sequence to be not Cauchy.

### 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 &#8804; x &#8804; 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

### Find the inverse of the given function

I need help finding the inverse of 3*2^(x-3)

### How human mortality is modelled mathematically / statistically?

Please advise what are the models/concepts. Thanks.

### 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.