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    Calculus and Analysis

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    Length of a curve

    Suspension bridge. The cable of the suspension bridge shown in the accompanying figure hangs in the shape of a parabola with the equation , where x and y are in meters. What is the height of each tower above the roadway? What is the length of z for the cable bracing the tower?

    A corner lot has dimensions 25 by 40 yards

    A corner lot has dimensions 25 by 40 yards. The city plans to take a strip of uniform width along the two sides bordering the streets in order to widen these roads. How wide should the strip be if the remainder of the lot is to have an area of 844 square yards?

    NORMAL Line Equation

    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)

    Working with Simple and Compound Interest

    If you borrow $500 from a credit union at 12% annual interest and $250 from a bank at 18% annual interest, what is the effective annual interest rate (that is, what single rate of interest on $750 would result in th same total amount of interest)?

    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)*

    Sketching 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.

    Differentibility of Functions and Limits

    Prove that if f is differentiable at x, then (see attachment) Also, show that for some functions that are NOT differentiable at x, this limit still exists. --- (See attached file for full problem description)

    Calculus 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). See the attached file.

    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

    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? (Complete problem found in attached file).

    Consider a parabola

    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)