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Calculus and Analysis

Vector-valued function word problem.

At time t = 0 a baseball that is 5 feet above the ground is hit with a bat. The ball leaves the bat with a speed of 80 feet per second at an angle of 30 degrees above horizontal. a) How long will it take for the baseball to hit the ground? b) Use the result in part a to find the horizontal distance traveled by the ball. Ple

Differential Equations : Thermodynamics of an Ideal Gas and Small Stage Efficiency

1. For a thermodynamic process involving a perfect gas, the intial and final temperatures are related by: where is the specific heat capacity of the gas, is the change of entropy and and are the initial and final temperatures of the process. Determine the value of if and . 2. The overall efficiency of a gas turbi

Solving a Differential Equation

Please see the attached file for the fully formatted problems.

Bernoulli Equation and Capacitor Current

Find the general solution of the Bernoulli equation: dy/dx -y/x = (y^4 cosx/x^3) A fully charged capacitor is discharged and the current i(t) flowing through a series of RC circuit at time t satisfying the equation: 1540 di/dt +800i =0. Given that E=115 V, draw the complete RC circuit and sketch the current (i) waveform.

Suppose and have radii of convergence R1 and R2, respectively, where R1 and R2 are non-zero real numbers. What can be said about the radius of convergence of the following series. Justify youtr answers, ? ? ? ? , where Please see the attached file for the fully formatted problems.

Solving trigonometric linear first order differential equations

Please solve the following differential equation, showing all steps and substitutions. Thank you. tanθdr/dθ + r = sin²θ

Solving a linear first order differential equation : e^(2x)y' + 2e^(2x)y = 2x

Please solve the differential equation below. Please show each step. Thank you. e^(2x)y' + 2e^(2x)y = 2x

Solving Differential Equations : 2 dy/dx - y = e^(x/2)

Please solve the differential equation below. Please show all steps in the solution. 2 dy/dx - y = e^(x/2)

Solving Differential Equations : &#8730;x dy/dx= e^(y+&#8730;x)

Please solve the differential equation below. Please show all steps in the solution. &#8730;x dy/dx= e^(y+&#8730;x)

Solving Differential Equations : dy/dx=x²√y, y>0

Please solve the differential equation: dy/dx=x²√y, y>0

Finding initial value of differential equations

Please find the initial value of this problem: d³θ/dt³=0; d²θ/dt²= -2; dθ/dt= -½; θ;=√;2 when t=0 Please show all steps. Thank you

Antiderivatives and Differential Equations : Finding the Initial Value

I am asked to find the initial value. The given information is: d²y/dx² = 0 dy/dx=2 y=0 when x=0

Solve differential equation xy' + xy + 2y - 2e^(-x) = 0

I need help with the problem! xy' + xy + 2y - 2e^(-x) = 0 I had a hard time figuring out how to solve it... please help!

Second Order Differential Equation : Separation of Variables

(1 + x^2 + Y^2 +(x^2)(y^2))dy = (y^2)dx

General Solution to Homogeneous Differential Equation

(y^2 + yx)dx + x(^2)dy=0

Present Value of Money and Calculus

Please answer the following questions: The Present value of money is the amount that you need to deposit now in order to have a desired amount sometime in the future . 1. What is the present value needed in order to have saved \$60,000 in five years, given an annual interest rate of 7% compounded monthly? 2. What is the

Volume of revolution..

Consider the function x=12(y^2-y^3). Determine why revolving this curve about the x-axis has a different volume than revolving about a line y=1.

Differential Equations : Equations of Motion, Laplace Transforms

Refer to figure 2 in attachment. a) Write the equations of motion for the mechanical system.****PLEASE SHOW YOUR FREE-BODY FOR EACH MASS****THANKS B) Take the Laplace transform of these equations, arrange them in matrix form, solve for the displacement x2(t), and find the transfer function T(s)= X1(s)/F(s) C) Using the co

Calculus : Value that allows for continuity at a point.

The function is given by the formula f(x) = (5x3 + 16x2 + 12x + 27)/(x + 3) when x<-3 and by the formula f(x) = -5x2 - x + a when -3=< x. What value must be chosen for a in order to make this function continuous at -3?

How does a bond's value change with the interest rate?

How does a bonds value change with the interest rate?

Differential Equation : Solve Using Classical Method; Identify Critically Damp, Overdamped or Under-Damped

X'' + 2x' + x = 5exp(-t) + t for t greater/equal to zero; x(0)=2; x'(0)=1 and identify critically damp, over-damped or under-damped (overdamped or underdamped). thank you

Length of a curve

Using the formula for the length of a curve y=f(x) from a to b L=&#8747;&#8730;(1 + (dy/dx)²)dx Find the length of the curve: x=(y³&#8725;6) + 1/(2y) from y=2 to y=3 Hint: 1 + (dx/dy)². is a perfect square

Identity Functions Detailed

Prove the given identity - Please explain in detail. 14. 2 cos x - 2 cos^3x = sin x sin 2x 16. cos (x-y)/cos x cosy = 1 tan x tany 20. sec x -cos x = sin x tanx 22. sin 2x = 1/tanx +cot 2x 23. If tan x = 5/12 and sin x>0 , find sin 2x 26. If sin x = -12/13 with pie <x<3pie/2, and sec y = 13/12 with 3 pi

Finding the Volume of Revolution Using the Shell Method

Using the shell method, find the volume of a solid generated by revolving about the y axis. The boundaries of the solid are: y=9x/&#8730;(x³+9) the x-axis the line x=3 Note: I received a solution to this problem from an OTA, but it appeared that the integration wasn't complete. I would like to see another OTA sol

Prove the following identities..."not an identity" is an option

1. cot²x-cos²x = cos²xcot²x 2. cotx = cscx/secx 3. tanx = sq.rt. sec²x-1 4. sinx/1-cotx + cosx/ 1-tanx = cosx + sin 5. cotx-1/1-tanx = cscx/secx 6. cosxsiny = 1/2 (sin(x+y) - sin (x-y))

Inverse Laplace Transforms and Convolution Integral

Find the inverse Laplace transform of the following: (a) 10/(s2+9) (b) 2e^-2s /(s+3) (c) .... (d) Find the inverse Laplace transform of F(s) using convolution integral where F(s) = .... Please see the attached file for the fully formatted problems.

Limits and L'Hopital's Rule (34 Problems with High Quality Solutions)

Find the limits using L'Hopital's rule where appropriate. If there is a more elementary method, consider using it. If L'Hospital's rule does not apply explain why. 1) lim as x approaches -1 (x^2 -1) / (x + 1) 2) lim as x approaches -1 (x^9 -1) / (x^5 - 1) 3) lim as x approaches -2 (x+2) / (x^2 +3x + 2) 4) lim as x approa

Graphing, Translation, Reflection, Domains, Limits, Derivatives

For the following graph the given functions on a computer screen, how are these graphs related? 1) Y=2^x, y=e^x, y=5^x, y=20^x 2) Y=3^x, y=10^x, y=(1/3)^x, y=(1/10)^x _______________________________________________________________________ Make a sketch of the function. 7) y=4^x-3 8) y=-2x^-x 9) y=3-e^x 13)