1. For the problem given below use the convolution theorem to write a formula for the solution of the I.V. problem in terms of f(t) y''-5y'+6y=f(t) y(0) = y'(0)=0 2. Use Laplace Transforms to solve the following equation t^2 y'-2y = 2 (no IC's)
Finding Vector Equation of a Plane and Cartesian Equation of a plane when three points of the plane are given. For complete description of the problems, please see the actual problems solved in this posting.
Question (i) Find the vector equation of plane which passes through the points (2,1,1) , (1,-1,-1) and (-1,1,2). Question (2) Obtain the Cartesian equation of a plane passing through three points (3,6,5) , (4,5,2) and (2,3,-1). The question file is attached.
A mass-spring system with damping consists of a 7- kg mass, a spring with spring constant of 3 N/m. a frictional component with damping constant 2 N-sec/m. and an external force given by f(t)=10 cos 10t N. Using a 10-ohm resistor construct an RLC series circuit that is the analog of this mechanical system in the sense that the t
Finding the value of a constant, when a unit vector is given, Finding unit vector parallel to the vector (a+b+c) when the three vectors a,b,c are given. Finding a unit vector parallel to sum of the given two vectors. (For detailed description of the problems, please see the Long Description of the Problems.
Q.2(a) Find the value of Lamda if Lamda(2i- 4j+4k) is a unit vector. (b) If a,b and c are any vectors such that a = ( 2 , 4 , - 5), b = ( 1 , 1 , 1 ), c = ( 0 , 1 , 2 ) find the unit vectors parallel to (a+b+c). (c)If r = xi+yj+zk then write the unit vector in the direction of r. (d)Determi
Solve the initial given value using the Laplace Transform Method: w" + w = t2 + 2 ; w(0) = 1 , w' (0) = -1 .
Please answer the following questions: 1. Sketch the graph of the parabola y= 3x^2 - 2x + 1. 2. Sketch the graph of the function y = sqrt(16 - 4x^2).
1.Find the particular solution that satisfies the initial condition. Differential Equation Initial Condition 2 2xy'-1nx =0 y(1)=2 2.Write and solve the differential equation that models the verbal statement. The rate of change of P with respect to t is proportional to 10-t.
Find the following limits as x approaches infinity: 1) x ^ (1/x) (1/x) is the exponent. It may be easier to read in the attached Word doc.
50 Problems Please see the attached files for the fully formatted problems.
Find the zero of the linear function f(x)=3x-12 Find the zeros of f(x)=x^2-2x-3 Find the vertex of f(x)=x^2-2x+4 Find the axis of symmetry of f(x)=x^2-2x+4 Find the zeros and state the multiplicity of each for f(x)=x^2(x+3)(x+1)^4 Find the zeros of f(x)=x^2-8x+12
1.) A deposit of S dollars that earns 100r% annual interest compounded continuously leaves a balance of P = 'Se' power of 'n' or ( 'Se' to the 'n') dollars after "t" years. a) What will an amount of $ 5000 grow to after 15 years at 10% annual interest compounded continuously? b) Determine the rate at which P is growi
In the posted problems, three vectors a = (3 , - 2 , - 1 ) , b = (1, - 2 , 4 ) and c = (3 , 2 , - 5 ) are given, and it is asked to find the equation of the plane containing the vector 'a' and parallel to the vectors 'b' abd 'c'. In the second problem the position vectors of 'A' and 'B' are given as 4i + j - 2k and 5i + 2j + k respectively and we have to find the equation of the plane passing through 'A' and 'B' and and parallel to the vector 3i - j + 4 k. In the third problem we have to show that r = (i - j) +  (2 i + k) and r = (2i - j) + (i + j - k) do not intersect.
Question (1): Find the equation of the plane containing the vector a = (3 , - 2 , - 1 ) and parallel to the vectors b = (1, - 2 , 4 ) and c = (3 , 2 , - 5 ) Question (2) : Find the equation of a plane passing through A and B whose position vectors are 4i + j - 2k , 5i + 2j + k respectively and parallel to the vector 3i
#(d^3z/dx^3) - 3(d^z/dx^2) + 2(dz/dx) = e^3x/(1 + e^x)
Calculus, Vector Product, Area of Triangle using Vectors, Volume of Parallelopiped using Vectors, Finding a Vector Orthogonal to a plane.
Question (1) a = (3 , 1 , 2 ) , b = ( - 1 , 1 , 0 ) , c = ( 0 , 0 , - 4 ) , then show that a × ( b × c ) ≠ (a × b) × c Question(2) Given P ( 2 , 1 , 5 ), Q = ( - 1 , 3 , 4 ) and R = ( 3 , 0 , 6 ), then find (a) a vector orthogonal to the plane through the points P,Q and R (b) Find the area of the triangle PQR
Determine whether the given vectors are orthogonal, parallel or neither. <-5,3,7> and <6,-1,2> <4,6> and <-3,2> -i + 2j + 5k and 3i + 4j - k 2i + 6j - 4k and -3i -9j +6k Find a unit vector that is orthogonal to both i+j and i+k. If a = <3,0,-1>, find a vector b such that comp_a b = 2 (component of b in the a direction
1. y'' + k*y = 0 BC: y'(0) = 0 y'(L) = 0 2. y'' + k*y = 0 BC: y(0) = y() y'(0) = y'() 3. y'' + k*y = 0 BC: y(0) = 0 y() +2*y'() = 0 4. y'' + 2*y' + (1+k)*y = 0 BC: y(0) = y(1) =0 Please see the attached file for
1.) Let f(x)=(the integral from 0 to x^2) sint dt. At how many points in the closed interval [0, square root of pi] does the instantaneous rate of change of f equal the average rate of change of f on that interval. keywords: integration, integrates, integrals, integrating, double, triple, multiple
Please explain how/why: lim x---> - 1 x^2 - 1 / x+1 How would this change if the 1 was positive?
1) a = (1, 2, -2); ||b|| = 6. What choice of b will make the dot product a . b the least possible? 2) The plane P pass through the point M (2, 3, 1) and is parallel to vectors u = (1, -1, 4) and v = (2, 1, 0). Find the distance from the point N (3, 2, 4) to the plane P. 3) Find an equation of the plane that passes through (1,
1) Find the equation of the line passing through the point (6, 1, 8) in the direction of the vector (-3, 4, -2). Write the equation in vector and coordinate form. 2) Find the equation of the line segment joining points (2, 4, 6) and (1, 7, 8), both in vector and coordinate form. Be sure to specify the set of possible values o
Determine the infinite limit #1)lim x-1/x^2(x+2) x->0, #2)lim csc x x->pi -, #3)lim ln(x-5) x->5+, #4)lim 6/x-5 x->5- #4) The slope of the tangent line to the graph of the exponential function y= 2^x at the point (0,1) is limx->0(2^x - 1)/x. Estimate the slope to three decimal places. keywords : find, findi
Find limit lim x---> - 4 x^2 - 16 / x+4 Please explain keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving
4. A retailer you spoke with in New York City's fashion district imports haute couture from European designers. One of the accommodations which must be considered when importing fashion from other countries is the difference in the size charts. A function that will convert dress sizes in the United States to those in Italy is
If y = XsinX prove that Y (X^2 + 2) - 2X dy/dx + X^2 d2y/dx2 = 0
(a) The function 1/t is continuous on the given interval, therefore integrable. The primitive is log(t). The primitive of exp(t) is exp(t). Therefore the integrals are: (b) The primitive of -cos(x) is -sin(x) anf the primitive of x is x2/2, therefore the integral equals: (c) We apply the so called Simpson's approximation:
Find the general solution to the following (d^4y/dx^4) + 4(d^3y/dx^3) + 8(d^2y/dx^2) + 8(dy/dx) + 4y=0
Find the general solution of the following (d^6y/dx^6) -3*(d^4y/dx^4) +3*(d^2y/dx^2) -y=0
Let s (n)= (sigma sign with n as upper bound and i=1 as lower bound) (1+(i/n))^2 * (1/n). Find the limit of s (n) as n approaches positive infinity.
Use the fundamental theorem of calculus to evaluate: (integral from 0 to 2) abs(x-1)*dx
Question: Evaluate the limit of e^(-x)*ln[x] as x approaches positive infinity. Please show all work.