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Calculus and Analysis

Weekly pass for hospital parking

A hospital parking lot charges $ 2.50 for the first hour or part thereof, and $1.25 for each additional hour part thereof. A weekly pass costs $50.00 and allows unlimited parking for 7 days. If each visit Johnny makes to the hospital lasts two and half hours, what is the minimum number of visits that would make it worthwhile to

Limit of the area of a polygon with n sides

--- The area of a regular polygon with n sides which is inscribed in a circle of a radius 1 is: (see attachment for equation) Find the limit as by substituting and writing the limit in terms of u, then evaluating that limit. Do you get the expected answer? Thank you! --- (Complete problem found in attache

Derivatives- Calculus I

Can you help solving the problem and show how to graph? --- Consider a parabola . How to find a, b, and c that satisfies the following: (see attachment). Graph the parabola. Thank you for your help! --- (Complete problem found in attached file)

Laplace Transformation

If f(t) is a period, continuous function with period T>0, show that its Laplace transformation is... (See attachment for full question)

Differential equation and spring

I am looking for a detailed solution. I need set up, solving, and final result. Therefore, I need solution of the second order DFQ. Finally for the description of the movement as time goes to infinity, I need what type of motion is that. a. An 8lb weight is attached to a spring suspended from the ceiling. When the weight come

Differential equations

I need to know how to find a particular solutions to an initial conditions. i know how to find the explicit solution of a differential equation but cannot remember how to find particular solutions. please show your working to help me understand. thanks Problems (also attached): Given the attached information: 1) So how

Initial value problem//Involving Laplace transformatins and partial fractions

A) Solve the Initial value Problem: y"+y=dπ(t)+d2π(t)+d3π(t)+......dnπ(t) ******dπ.- meaning delta sub index phi******** b) Graph the solution on the interval [0,3π] c) Discuss the behaviour of the solution in relation to the equation. I am looking for a solution for this problem. I need the

Solve and Explain Three Integrals

∫ (x^5)/[(1+x^3)^(3/2)] dx ∫ {square root of [(x+3)/(x+1)]}dx ∫ (cot^3 v)[(csc v)^(3/2)] dx (I will use the $ sign for the integral sign) Problem #1: $ (x^5)/[(1+x^3)^(3/2)] dx the power 3/2 in the denominator is throwing me off greatly, as is the greater power (x^5) in the numerator. attempt 1

Damping and Resonance Problem : Forces and Displacement

A seismograph is a scientific instrument that is used to detect earthquakes. A simple model of a seismograph is shown below. It consists of a particle of mass m to which a pointer is attached. The particle is suspended by a spring of natural length lo and stiffness k and a damper of damping constant r from a platform of height d

Differential equations

I am looking for the best statements about solutions and how is the statement supported... Please see attached.

Second Order

Find general solution of a second order differential equation.

Graphical methods

Ref. M4. use graphical methods to find the differential coefficient of simple sinusoidal and exponential functions. Please help with correct steps and formulas to get answer. Please see attachment

Inverse Function

Find the equation of the attached inverse function, if the function is invertible.

Vertex and intercepts

Find the vertex and intercepts for the quadratic function and sketch its graph y=x^2+4x

Instabilities exam paper - A2

Please work on A2 from the attached exam practice paper. A2. The population of birds on an island is described by the following model... Please see attached for full question.

Differential equation

I am currently having trouble with some of this stuff, and my job requires that i learn this all again so i was wondering if i could get some help t(t-3)y''+2ty'-y=t^2 y(1)=yo, y'(1)=y1 y1 and yo are real constants find the interval of the unique solution Also find the interval if the above initial condition changes to y(