1. Two well-mixed tanks are hooked up so that water with 2 pounds of salt per gallon flows into the first tank, well - mixed water flows out of the second tank, water flows from the first tank to the second tank, and water flows from the second tank to the first tank. All flows are constant. Determine how much water is in each of the two tanks, given if x is the amount of salt in the first tank and y is the amount of salt in the second tank then 3x 2x - 3y. The answer should -x + y + 30 and 6y' be 45 gallons in the first tank and 30 gallons in the second tank. =

Q: 2.2.1. Prove that each of the following sequences converges to zero. write a) xn =…

A: We have to show that the following sequences  converge to zero.

Q: An important tool in archaeological research is the radiocarbon dating developed by the American…

A: From the given information, we know that the rate of decay of carbon-14 () is proportional to the…

Q: Use the superposition principle to solve Laplace's equation (1) in Section 12.5 a²u a²u + -0, 0<x<a,…

A:

Q: box. The dimensions of a closed rectangular box are measured as 90 centimeters, 50 centimeters, and…

A: Given that :The dimensions of a closed rectangular box are measured as 90 centimeters, 50…

Q: 10. Consider the curve X(t) = (t², t³ - at), where a is a real number. Calculate the curvature…

A: The curve is :The aim is to calculate the curvature function

Q: = Problem #4: Find the equation of the plane that is tangent to the surface f(x, y): much as…

A: The equation of tangent plane to the surface  at point  isWe have given:

Q: Succulent Citrus produces orange juice and orange concentrate. This year the company anticipates a…

A: The objective of this question is to determine the number of quarts of orange juice and orange…

Q: Write the level surface 4 = 2x² + 5y + √√z as the graph of a function f(x, y).

A: Given, an equation:It is required to express the level surface as the graph of a function , meaning…

Q: (a) Prove that Σ³ = n²(n+1) ². j=1 (b) Evaluate fr³ de directly from the definition, without using…

A:

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A: For the Newton's law of cooling :The ambient temperature is :The proportionality constant is :The…

Q: A graph of y=x² + 4x²-3x-18 is shown. Use the graph to solve x² + 4x² – 3x-1820. 20 10 _y=x²³ + 4x²…

A:

Q: Which 4-tuples a 0<a<b<c<d<6}. are int the relation {(a, b, c, d)|a, b, c, d are integers with

A: We need to identify the tuples of the integer relation .Let .

Q: Solve for u(x, t): 1 3ux + 4u=0, u(x, 0) = 1 + x²

A: Given that the differential equation is:                             To find the solution of the…

Q: Let G be a simple graph. Show that the relation R on the set of vertices of G such that u Rv if and…

A: Given: A simple graph is G.To prove: That the set of vertices of G is such that  if and only if…

Q: a company that supplies clean water to 9 villages in the town of Seroja. The flow of water that can…

A: Network diagram for the pipeline with the flow of water to each village.The aim is to determine the…

Q: Which random graph G(N, p) has (k) and variance o² of the degree distribution given by o² = 20?.…

A: We have the following relations between the given quantities:Given values:Solve for and :For :  For…

Q: Is 1326 a a triangular number? What about 1.37.8?

A: 1326 is the 51st triangular number because  and  is 1 more than 51.Similarl,1378 is the 52st…

Q: Trudy earns $6,300 per month as a vice president at a sales company. Calculate her yearly salary.…

A: The objective of this question is to calculate Trudy's annual salary based on her monthly earnings.

Q: Is the following 2 1 1 -3 0 2 A = matrix A strictly diagonally dominant? -1 1 7

A: The given matrix .The objective is to determine whether the matrix is strictly diagonally dominant…

Q: Given that y = x is a solution of ď²y (x²(5 + x²)). dx² (15x) dy + (15)y=0, in x > 0, find another…

A:

Q: (2) Consider the following LPP in canonical form: maximize subject to a₁x₁ ++ anxn+y=t=b x1,, xn, y,…

A: The objective of the question is to find all Basic Feasible Solutions (BFS), basic directions at the…

Q: Find the least residue of the (multiplicative) inverse of the product modulo 947. (Note that 947 is…

A:

Q: (1.) (a. The curve of intersection of the sphere of radius √8 centered at the origin and the cone…

A:

Q: Seven office mates, three women (Fran, Gladys and Helen) and four men (John, Karl, Leonard and…

A: The answer is iv. Karl.  Here is how I justify my answer:Since it is Wednesday, Fran must eat at a…

Q: 4-10. Find the optimal value of the objective function for the following problem by inspecting only…

A: The primal problem is:Minimize: Subject to:X1, X2, X3 ≥ 0The dual problem is formulated as…

Q: Prove that VÃZ,n,m=N(x²)m = xmn¸

A:

Q: du du 6-y+x² = 0 dx dy Solution of Partial Differential equation By

A: As per our company's guidelines we are supposed to answer only first question. Kindly repost other…

Q: Using Fermat's little theorem, find the least residue of modulo 389. (Note that 389 is prime.)…

A: Since you have posted multiple questions, we will provide the solution only for the first question…

Q: 3. Determine the amplitude of the sinusoidal function y = −3 sin[2(x − 60°)] + 1. a. 2 -3 b. 3 60°…

A:

Q: 4. Calculate Res z+1 z²+9 -3i

A: The answer is (1/2)+(i/6)Explanation:Step 1: Step 2: Step 3: Step 4:

Q: The following second-order ODE ay"+by+cy = 4x + (sin.x) e* has a complementary solution given by ye…

A:

Q: 12 Find the independent term of x in development (x² − ¹)²

A: We have to find the independent term of x in the expansion of (x2−1x)12, we'll use the binomial…

Q: 8 Odd Half - Range Extension Create the odd function go(t) by flipping fo(t) 180° around the…

A: A function f(t) is said to be an odd function if f(−t)=−f(t).Given thatf0(t)={8t,0≤t≤18,1≤t≤4g0(t)…

Q: (x, y, z) = 6xy + 4yz + 6y-3z² - y² subject to x + torder conditions. are of the extreme points.

A: Consider the function  subject to .Let .

Q: Need help with these two Intro to Elementary Number Theory Homework problems.

A: (601−1)!≡600 modulo 601(816−1)!≡0 modulo 816Explanation:

Q: 7. Obtain the amplitude, vertical shift, period, Dr. R. and function graph f(x) = -3 cos(2x + n)

A:

Q: (a) Let F = 2xz²i+j+xy³zk and f(x, y, z) = x²y. Compute the following quantities: (i) Vf (ii)…

A: As per our guidelines we can answer only 1 question and 3 subparts of a given question so kindly…

Q: Hi I need help with 4a) and c)

A: a) The power series with the specified properties is f(z) = Σ(n=0 to ∞) [(z - 3i)n/7n].b) The power…

Q: #3: Find the maximum of f(x, y) - 19 In(18x96) +43 subject to x² + y² = 25, x > 0, y > 0.

A:

Q: Find the second and third derivative of the following 893 1. y 12x6x7 +17x5-6x4 +24x³ THE 2. y =…

A: Derivative of all functions continuously 3rd order And we get,

Q: 1. Find the where the function is increasing, decreasing, has relative extrema, is concave up or…

A: Given, a function .It is required to find the intervals where the function is increasing,…

Q: 28. Show that tan z = sin(2x) + i sinh(2y) cos(2x) + cosh (2y)

A: We can show the given identity.

Q: f = x² + x³x²+1, g = x³ + 1 in Q[x];

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Use a symbolic argument in Problems 29, 30, 31, and 32 to determine if the argument is valid or…

A: Given the statement that all mathematics are eccentrics, all eccentrics are rich, therefore all…

Q: I need help with this complex variable question

A: 2.{zn​} converges to z if and only if ∣zn​−z∣ converges to 0Explanation:

Q: Determine the coordinates of the center of the circle and determine its radius if its equation is x2…

A: To determine the center and radius of the circle represented by the equation , we first need to…

Q: B₂ = {(2₂1 X12 X22 |xij≥0 for i, j = 1, 2, X11 + 12 = 2, X21 + x22 = 2, x11 + x21 = 1.5, x12 + x22 =…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts…

Q: (b) Tiff becomes a human missile after 6 seconds on the ride. Find Tiff's coordinates the instant…

A: (a) Tiff's coordinates at time  seconds after she starts the ride are given by:(b) To find Tiff's…

Q: 1. For each solution. congruence determine whether there is a J X² = -1 (mod 397) (397 is prime) CC…

A: We shall be using the result regarding the value of legendre symbol

Q: Problem #1: If f(x,y) is differentiable near (x, y) = (a, b), and u is any unit vector, consider the…

A: