A tank contains 100 kg of salt and 2000 L of water. A solution of a concentration 0.025 kg of salt per liter enters a tank at the rate 5 L/min. The solution is mixed and drains from the tank at the same rate. (a) What is the concentration of our solution in the tank initially? concentration = (kg/L) (b) Find the amount of salt in the tank after 1 hours. amount (kg) %3D (c) Find the concentration of salt in the solution in the tank as time approaches infinity. concentration = (kg/L)

Q: Find the transition matrix: (a) From the basis B = {(1,0, 2), (0, 1, 3), (1, 1, 1, )} to the basis B...

A: We have to find the transition matrix from the basis B to the basis B'. We have to write the vectors...

Q: Now that we have figured out how to do step 1, we are going to try and do steps 1 and 2. Given the d...

A:

Q: Let p and q be propositions. Then p →1 19 A(p → q)] is a contradiction contingency tautology

A:

Q: The value of function f(x) = sin x (1 + cos x) is maximum when x is equal to

A:

Q: 27. Find the Inverse Laplace Transform of the following: 150 d. (s? + 2s + 5)(s? – 4s + 8)

A:

Q: What is the difference between the maximum and minimum of the quantity x2y2/87, where x and y are tw...

A:

Q: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = <0, 1, 2>  and  w = <1, 0, 1> Let av + bw = 0 => a(0, 1, 2) + b(1, 0, 1...

Q: -1, 1] then abs on is

A:

Q: If a student is to answer any six problems on a test consisting of nine problems, in how many differ...

A: Here the student is free to answer any 6 questions out of 9 problems.  So, we take the combination.

Q: 5. Consider the matrix in echelon form 1 2 0 0 1\ A = |0 1 0 0 0 1 0, 0 0 1 Write a basis for the Nu...

A: To find the basis of the Null(A) we need to solve the system of equation AX=0

Q: 2 Let f(x,y,z) = 4x + 2y +z +7 and P be the point (x,y,z) = (1,1,1). (i) Find a unit vector n in the...

A:

Q: (b) Sketch the graph of a function that has a local maximum at 3 and is continuous but not different...

A: To sketch the graph of the function which is local maxima at 3 and not differentiable at 3

Q: HiW Are the ollowing complex functions or not. auna lytic eire fiz) = é @ $(Z) = Z Z*.

A:

Q: 1. Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduce...

A:

Q: L{t e¬at } =

A:

Q: Consider the differential equation (E): x²y"-xy' +y 0. Given that y, x and y, xlnx are solutions of ...

A: Given solutions are y1 = x  and  y2 = xln(x)

Q: 3 If the characteristic roots of 2 7 are A1 and A, the characteristic root of 7 are - 2 3

A: Given matrix is 3725 with λ1 and λ2 its eigen values.

Q: The approximation of the solution x*of the equation x2 In(x + 1)- x-2 0 accurate to within 102 using...

A:

Q: The approximation of the solution x*of the equation x2 In(x + 1)- x-2 0 accurate to within 10 using ...

A: Here  x2ln(x+1) - x - 2 = 0Let  f(x) = x2ln(x+1) - x - 2

Q: Determine the graph of the equation. x² +y? - z? = 16 Choose the correct graph of the equation. O A....

A: 3D. Graphing r

Q: Find the average value of f(x,y) = sin (x +y) over a. the rectangle 0<x<n/6, 0sys11r/6 b. the rectan...

A:

Q: Determine the solution of the initial value problem 1. 5y" + y' =-6x, 2. y" + 4y' + 5y = 35e4x, y(0)...

A:

Q: 6s+21) a Tost +5) 35+5

A:

Q: az that satisfy a, -a, = a, – a,. az 3. In R', let Wbe the subset of all vectors v = a4 a) Show that...

A:

Q: At the stationary point (x0, Yo) the function f(x, y) has the Hessian matrix 4 3 H= 3 -4 Then: Selec...

A:

Q: 13 16 26 and T then the standard matrix of T is

A:

Q: 1. Which of the following sets of vectors a = of R (n 2 3)? (a1, .. . , an) in R are subspaces (a) a...

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for you...

Q: Compute for the hypothetical total area and actual size of the sketch map above using the scale of 1...

A: Solution

Q: (b) The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% p...

A:

Q: Consider a rectangle of sides ? and ? with fixed perimeter of 40 units. Find the maximum and minimum...

A: Consider a rectangle of sides ? and ? with fixed perimeter of 40 units. Find the maximum and minimum...

Q: Va vector space? Show the detailed solution for each property.

A:

Q: What is the general solution to the differential equation dy = dx + 3y tan x ? sin³x y cos³x = sin x...

A: Correction : In right hand side of given differential equation is {dx + 3y tan x dx}

Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the...

A: If a set of vector spans a subspace which is linearly dependent, then we can find a subset of the se...

Q: Which Riemann sum represents the illustration shown?

A: This is the problem of Reiman Sum.

Q: find the laplace transform of the equation: f(t)= 2t^3 e^-4t

A:

Q: Consider the following system of four equations. You are given two solutions X1 and X2. Generate fou...

A:

Q: 1. Prove or disprove. a) det(A+B) = det(A) + det(B)

A:

Q: Complete the following statement. If m|n and n Im , then.. а. m= - n b. m=+/-n c. None of these d. m...

A:

Q: Problem 1.27. Find the in-degree and out-degree of each vertex of the following directed graphs a V3...

A:

Q: p and 4 ave selan function, and cs constant, Pmve that,

A:

Q: Does the following series converge or diverge? n° Σ n=1 O The series diverges. The series converges.

A: ∑n=1∞an=∑n=1∞nn8n2 Theorem: let ∑n=1∞an,be the series L=limn→∞an1n then, If L&lt;1 the series is abs...

Q: Find the unknown variable: nC5 = 126 Vour a ncwor

A: We have to find the value of n such that it satisfies the equation C5n=126. It is clear that the giv...

Q: Let R[x] be the set of all expressions a = ao+ajx+a2x² + ……=£a;x ....- i=0 where a¡ E IR for all non...

A:

Q: Let W be the set of all vectors of the form 5t – (3r + 5s) 3r + 2t 5s – r +t r – 3s with r, s and t ...

A:

Q: (d) Consider the system of linear equations Ax = b. Without actually computing the solutions of the ...

A: (d) The reduced row echelon form of the given matrix is 100010001

Q: 1. A curve passes through the points (1, 0.2), (2, 0.7), (3, 1), (4, 1.3), (5, 1.5), (6, 1.7), (7, 1...

A:

Q: a, az B. In R*, let W be the subset of all vectors v = that satisfy a, -a, = a, –a,. az a) Show that...

A:

Q: Which among the following statements is true? * Every conditional statement is logically equivalent ...

A: The 1st two statement is not correct since we know that A conditional statement is logically equival...

Q: 3) a) i) Calculate the simple interest earned if a deposit of  $ 200,000 is left for 12 years at an ...

A:

Q: Suppose f : (a, b) → R is continuous at every point in the open Question 3 interval (a, b), and that...

A: