### Volume of Water in a Conical Vessel

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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

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

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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.

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

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

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

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

Please solve the differential equation below. Please show all steps. dy/dx=(2x²+1)/(xe^y)

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

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

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

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

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

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

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.

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

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 bonds value change with the interest rate?

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

Using the formula for the length of a curve y=f(x) from a to b L=∫√(1 + (dy/dx)²)dx Find the length of the curve: x=(y³∕6) + 1/(2y) from y=2 to y=3 Hint: 1 + (dx/dy)². is a perfect square

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

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/√(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

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))

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.

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

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)