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    Calculus and Analysis

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    X-Coordinate of Centroid of Closed Region

    What is the x-coordinate of the centroid of the closed region Please see attachment for function and region description. Please explain why the answer is correct. Thank you!

    Differential Equations : Particle Position at Time

    2. A particle moves along a straight line so that its acceleration at time t seconds is (t + 1)2 cm/sec2. The particle's position at time t = 0 is at the origin, and its initial velocity is 1 cm/sec. What is the position of the particle, in cm. at time t seconds? A.((t+1)4/12)+(2/3)t-1/12 B.((t+1)4/12)+(2/3)t+1/12 C.((t+1

    Differential Equations : Population Growth

    9. The rate of change of the population of a town in Pennsylvania at any time t is proportional to the population at that time. Four years ago, the population was 25,000. Now, the population is 36,000. Calculate what the population will be six years from now. A. 43,200 B. 52,500 C. 62,208 D. 77,760 E. 89,580

    Solve a Differential Equation

    8. What is the solution of the differential equation dy/dt = 4y2t3, subject to the condition y(1) = 1? A. y = 1/(2-t4) B. y = 2 - 1/t4 C. y = t4 D. y = 1/t4 E. y = e^(1-t2)

    Differential Equations : Radioactive Decay

    The rate of decay of a radioactive substance is proportional to the amount of the substance present. Two years ago there were 5 grams of substance. Now there are 4 grams. How many grams will there be 4 years from now? A. 16/25 B. 2 C. 64/25 D. 16/5 E. 25/4

    Solve the Differential Equation

    Which of the following is a solution to the differential equation: ylny + xy' = 0 for x > 0 ? A. xlny = 1 B. xylny = 1 C. (lny)2 = 2 D. -y(lny)(lnx) = 1 E. lny + (x2/2)y = 1

    How do I solve this problem of second - degree equations?

    Sketch the graphs of each pair of circles to determine the number of points of intersection. If the circles are tangent or fail to intersect, say so. Then solve the system. 2 2 2 2 x + y - 4y= 0, x = y - 2x = 4 How do I go about solving?

    Normal Modes : Second Order Simultaneous Equations

    This question is concerned with finding the solutions of the second order simultaneous equations where a = 38, b = -9, c = 378, d = -79 (i) Find the particular solutions to the differential equations which satisfy the initial conditions x = -10 and y = 7 at t = 0 together with the condition at t = 0.. For this part

    Prove Using the Chain Rule

    Please see the attached file for the fully formatted problems. Let x,y denote Cartesian coordinates and denote polar coordinates, and let . Using the chain rule show that (you may assume that ). Hence show that

    Rate of Change of Volume Given Rate of Change of Height

    The height h of a right circular cone is 20 cm and is decreasing at the rate of 4 cm/sec. At the same time, the radius r is 10 cm and is increasing at the rate of 2 cm/sec. What is the rate of change of the volume in cm3/sec? (Note: The volume of a right circular cone is V = 1/3p r^2h.)

    Find the Limit of Equation

    Please see the attached file for the fully formatted problem. If lim x --> 0 f(x) = 3 then lim x--> 0 (e^(2x)-1)/(x f(x)) = ?

    Heat Diffusion Equation and Standard Heat Equation

    A) Let the temperature u inside a solid sphere be a function only of radial distance r from the center and time t. Show that the equation for heat diffusion is now: {see attachment}. This is not an exercise in doing a polar coordinate transformation. First you should derive an integral form for the equation by integrating over a

    Business Calculus Functions

    Given the following table...(a) Is y a function of x? Explain your answer. (b)Is x a function of y? Explain your answer. (See attachment for full question) Hi, I am having trouble doing these problems listed below. Please show me how to solve these problems for future reference. Thank you very much. I would like for you

    The problems are from Boundary Value Problems

    The problems are from Boundary Value Problems. Undergrad 400 level course. Mainly uses partial differential skills. Some problems might require using MATLAB. Please explain each step of your solutions. Thank you very much.

    The problems are from Boundary Value Problems

    The problems are from Boundary Value Problems. Undergrad 400 level course. Mainly uses partial differential skills. Some problems might require using MATLAB. Please explain each step of your solutions. Thank you very much.

    Rate of Change of Height of Cone

    Gravel is dumped from a conveyor belt at the rate of 30 cubic feet per minute and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and heght are always equal. How fast is the height of the pile increasing when the pile is 10 feet high? include the correct units in your answer. Let h=the heig

    Boundary Conditions for Transport Phenomena

    In solving transport phenomena problems, we use "boundary conditions" and "initial conditions". In mathematical terms, (that is, types of variables), what are "boundary conditions" and what are "initial conditions"

    Differential Equation into Transfer Function

    Transform the attached differential equation into a transfer function and find the homogeneous solution to the differential equation from the transfer function. See the attached file.

    Advanced Calculus Analysis : Cauchy and Convergent Sequences

    We proved the following theorem in the class: "If a>0 and if a sequence... is covergent, then the sequence... is convergent." In proving this theorem, we proved that... is Cauchy instead of proving it converges directly. Why did we have to do that? Please see attachment for full question.