Calculus - series
I'm getting this answer wrong, can someone please help show me what i'm missing?? thank you :) Infinity of the summation n=0: [(-1)^n pi^(2n)] / [6^(2n) (2n)!] this is my work: [(-1^0) pi^(2*0)] / [6^(2*0) (2*0)!] + [(-1^1) pi^(2*1)] / [6^(2*1) (2*1)!] + [(-1^2) pi^(2*...
Math
i'm a bit stuck with this.. 145/18 = x + x^2 what does x equal to? multiply each term by 18, then re-arrange to get 18x^2 + 18x - 145 = 0 This quadratic does not factor, so use the quadratic formula to get your two answers.
Math/Physics
Please check my work below and comment. A tank initially contains 80 gallons of fresh water. A 10% acid solution flows into the tank at the rate of 3 gallons per minute. The well-stirred mixture flows out of the tank at the rate of 3 gallons per minute. Find the amount of acid...
Math/Physics
I am given a damping constant of 20 dyne*sec/meter...do I need to convert this if the rest of my givens are, for mass = 2kg, k (spring constant) = 82 N/m. I am trying to find the equation of motion of a spring but cannot solve it until I know how to convert/if I need to conver...
Math/Calculus
Please check my work and correct any errors/point out any errors. Thanks. Solve the initial-value problem using the method of undetermined coefficients. y''-4y=e^xcos(x), y(0)=1, y'(0)=2 r^2-4=0, r1=2, r2=-2 yc(x)=c1*e^2x+c2*e^-2x yp(x)=e^x[Acos(x)+Bsin(x)] y'p...
Math/Calculus
A series circuit contains a resistor with R = 24 ohms, an inductor with L = 2 H, a capacitor with C = 0.005 F, and a generator producing a voltage of E(t) = 12 sin(10t). The initial charge is Q = 0.001 C and the initial current is 0. (a) Find the charge at time t. 2Q"+24Q...
Math/Calculus
Solve the initial-value problem. Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else? Thanks. y''+4y'+6y=0, y(0)=2, y'(0)=4 r^2+4r+6=0, r=(-4 +/- sqrt(16-4(1)(6))/2 r=-2 +/- sqrt(2)*i , alpha = -2, beta = 2(sqrt(2)) y=e^-2...
Math/Calculus
Please take a look at my work below and provide a good critique: Solve the differential equation using the method of undetermined coefficients or variation of parameters. y'' - 3y' + 2y = sin(x) yc(x)= c1*e^2x+c2*e^x y"-3y'+2y=sin(x) r^2-3r+2=0 (r-1)(r-2)=...
Math/Calculus
A spring with a 4 kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t. Here is my work so far: 2...
Math
A series circuit contains a resistor with R = 24 , an inductor with L = 2 H, a capacitor with C = 0.005 F, and a generator producing a voltage of E(t) = 12 sin(10t). The initial charge is Q = 0.001 C and the initial current is 0. Find the charge at time t. --------------------...
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