# Mathematics and Statistics

## Differential equation and explicit solution

The problem is: dx/dt = (x-1)(1-2x); ln {2x-1/x-1} = t To solve this problem I must, first, verify that the indicated expression is an implicit solution of the given first-order differential equation then find at least one explicit solution. The last element of the solution is to use a graphing utility to obtain the graph […]

## Calculate the Probability for a Silver Dollar Flipped Twice

A silver dollar is flipped twice. Calculate the probability of each of the following occurring: a. a head on the first flip b. a tail on the second flip given that the first toss was a head c. two tails d. a tail on the first and a head on the second e. a tail […]

## Advantages of heuristics and algorithms in problem solving

During problem solving, do you use primarily algorithms or heuristics? What are the advantages of each? Both have advantages and are useful for different situations and each relies on different type of knowing. Objective knowing, which uses systems and logic, is better paired with algorithmic problem solving.This includes formulae and theorems that have been tested […]

## Domain and range of y=2x – 3

y=2x – 3 Solution Summary The solution gives the domain and range of y=2x – 3.To continue with the answer check on topwriters4me.com/

## Conservation of Momentum and Collision Review

1. A car crashes into a wall at 25 m/s and is brought to the rest in 0.1 s. Calculate the average force exerted on a 75-kg test dummy by the seat belt. 2. A railroad diesel engine weighs four times as much as a freight-car. If the diesel engine coasts at 5 km/h into […]

## The probability of passing

I’m having trouble with this problem: A student is taking two courses, history and math. The probability the student will pass the history course is .60 and the math is .70. The probability of passing both is .50. What is the probability of passing at least one? Solution Preview Please see the attached file. A […]

## Use Parseval’s equality

We are using the book Methods of Real Analysis by Richard R. Goldberg (See attached file for full problem description) — 12.5-2 Show that the Fourier series for is a) Use 12.5E to show that Fourier series at t=0 converges to . Deduce that 12.5E: Theorem. Let ( this means the function f and the […]

## Real-Life Applications of Complex or Imaginary Numbers

When solving a quadratic equation using the quadratic formula, it is possible for the b2 – 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i). […]

## Advantages of heuristics and algorithms in problem solving

During problem solving, do you use primarily algorithms or heuristics? What are the advantages of each? Both have advantages and are useful for different situations and each relies on different type of knowing. Objective knowing, which uses systems and logic, is better paired with algorithmic problem solving.This includes formulae and theorems that have been tested […]

## Variance and standard deviation – a real world example

How may variance and standard deviation be applied to a real-world business-related problem? Provide a specific application in which these measures are useful. Solution Preview Variances and standard deviations are very useful in business. Among many of their uses, finance is probably the single most important area where these are needed. First, you should know […]

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