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Calculus and Analysis

Modeling Data for Linear Functions and Maximizing Profit

1960 88 1970 121 1980 152 1990 205 1997 217 a) Model the data with two linear function. Let the independendt variable represent the number of years after 1960. b) With each function found in part a), predict the amount of maunicipal solid waste in 2005. c) Which of the two models

Sand falls from an overhead hopper to form a right circular cone. If the cone formed has an angle theta find the rate of change of volume with respect to height? If the height is changing at 2cms per minute, what volume of sand is falling from the hopper when the height of the cone is 3 meters? (The volume of a cone is (1/3)pir2h where h is the height and r is the radius.)

Sand falls from an overhead hopper to form a right circular cone. If the cone formed has an angle theta find the rate of change of volume with respect to height? If the height is changing at 2cms per minute, what volume of sand is falling from the hopper when the height of the cone is 3 meters? (The volume of a cone is (1/3)pir2

To get to work Sam jogs 3 Kilometers to the train...

To get to work Sam jogs 3 Kilometers to the train, then rides the remaining 5 kilometers. If the train goes 14 kilometers per hour faster than Sam's constant rate of jogging and the entire trip takes 45 minutes, how fast does Sam jog?

See attached files

Several questions: 1. If a ball is thrown straight up in the air with an initial velocity of 90 ft/s... (See attached file for full problem description)

Normal line

The derivative of 1/sqrt(x) is -1/2(x^3/2), Give the equation of the NORMAL line at x=1

Intersection and distance

1. Find the intersection point of the line (x-1)/2=(y+1)/3=z-2 and the plane 2x+y-z=17. 2. Find the distance from point Q(1,-2,3) to the plane 2x-y-z=6. Need steps and solutions.....Thanks!

Equation for line and plane

1. Find an equation for the line passing through the points P(1,-1,1) and Q(3,1,-2). 2. Find an equation for the plane containing points P(1,0,0), Q(0,-1,0), and R(0,0,-1). Need steps and solutions. Thanks a bunch!

Spherical polar coordinates

Please help...this is a revision question very likely to appear in my exam next month but I do not understand it! (See attached file for full problem description)

Finding a particular solution of a differential equation

I already solved the homogeneous portion, and I need help solving the particular solution and of course combining the two to get the entire solution to the differential equation. Not too difficult - see attachment. Please use equation editor if possible. Thank you. --- Given that: dMS/dt = m(MN - MS) - pMS¬

Radius of convergence

(See attached file for full problem description) --- Find the radius of convergence of the following series...(see attachment for equation) ---

Differential Equations : The Contraction Mapping Theorem

1). Define T : C[0,1] --> C[,1] by (Tx)(t) = 1 + integral from 0 to 1 x(s)ds. Is T a contraction? ( Please justify every step and claim, I want a proof not a yes or no only). P. S. I believe C[0,1] is the set of all the continuous functions on [0,1]. 2). Consider the operator in C[0,1], Ty(t) = integral from 0 to t (t-s)*

Find and sketch level curves (isobars)

This question relates to a section that deals with basic vector calculus and introduces partial derivatives. Here is the question: Consider the scalar field (pressure field) given by f(x,y,)=9x^2 +4y^2. Q: Find the isobars (curves of constant pressure) and sketch some of them.

Calculus I Graph Antiderivative

Consider the graph of f(x): a)Can you draw a graph of F(x), the antiderivative of f(x), where F(0) = 1. b) Draw a graph of f(x).

Derivatives and Application of the Derivative

F(t) = 10,000 / 10 + 50e ^-0.5t HOW do I obtain the derivative? What is the "e" portion of the problem? I know the derivative = 250,000e^-0.5t/ (10+50e ^-0.5t)^2 Please describe in detail the steps taken to arrive at this answer. For example, Why is the top of the equation 250,000e^-0.5t? Why is the bottom (10+50e^-0

Differential Equations: Solution to Heat Equation

Consider the heat equation delta(u)/delta(t) = (delta^2)(u)/delta(x^2) Show that if u(c, t) = (t^alpha)psi(E) where E = x/sqrt(t) and alpha is a constant, then psi(E) satisfies the ordinary differential equation alpha(psi) = 1/2 E(psi) = psi, where ' = d/dE is independent of t only if alpha = - 1/2. Further, show th

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)