A tank initially contains a solution of 6 pounds of salt in 40 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 9 gal/min, and the resulting solution leaves at the same rate. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t). Q'(t) = (b) Find the quantity Q(t) of salt in the tank at time t > 0. (c) Compute the limit. lim Q(t) = 0077 Submit Question

Q: Compute all first and second order partial derivatives of f(x,y)= e siny. Verify that Clairaut's…

A: We have to find the first order and second order partial derivatives of the given function. And also…

Q: 11. La formule algébrique convertissant les degrés Fahrenheit en degrés Celsius et les degrés…

A: The formula for converting Fahrenheit to Celsius is given by…

Q: Determine whether the equation is exact. If it is, then solve it. (- sinxsin y-2x)dx + (cos x cos y…

A:

Q: 43. Find the first partial derivatives f(x, t) = e-t sin(x) g(x, y) X (x + y)² h(x, y) = tan ¹(y/x)

A:

Q: (b) Suppose that W is a subspace of R" and that {u, v, w} is a basis for W. Prove that (u, v) does…

A:

Q: Given F = (2-2yz)i + (y+xz)j + (xy + z2)k and S the surface z² = x² + y² where 0 ≤ % ≤ 4. Use…

A:

Q: (a) show that the set of vectors in Rn is orthogonal, and (b) normalize the set to produce an…

A:

Q: Let {x} be an ARIMA process (2,1,0) given by: (1-0.8B +0.25B²) VX₁ = Zt {Z}~WN(0,1) Determine the…

A: Given:  be an ARIMA process  which is given by: {Z_t}~WN(0,1) To Determine: The Forecast function

Q: Consider y" - 4y + 5y = 0. a) Determine the characteristic equation. b) Determine the general…

A:

Q: To complete these problems, you must first determine whether a given statement is true and, if so,…

A:

Q: 8 1 x+2 2 x² +2 xp..

A: The formula of Midpoint Rectangles is  , where  and

Q: Suppose A is a 4 x 4 coefficient matrix. If possible, find the entries of a matrix T that perform…

A:

Q: Show that the set B = {x² - -x+1, 3x² + 4, x - 2} is a basis of the (real) vector space of…

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

Q: (x² - 1)y" + 4xy + 2y = 0, y(0) = 1, y'(0) = -1 ∞ This problem has a series solution of the form y =…

A:

Q: 3. Find solution of the differential equation; x x(0) = x ' (0) = = 0 and Laplace transform…

A: Introduction: Laplace transform is named in honour of the great French mathematician, Pierre Simon…

Q: a. Calculate the determinant of A by hand. b. Use Python to calculate the determinant of A for ε =…

A:

Q: In exercises 1-10, classify each of the following integral equations as Fredholm or Volterra…

A: Let  us consider the integral equation : 1) If then (1)  is  called homogeneous integral equation.…

Q: Find the minimum and maximum values of the function f(x, y, z) = x² + y² + z² subject to the…

A:

Q: 2. Let f(x) = 3 - 2-ª. a) Find the largest interval containing x = 3 in which f is one-to-one. b)…

A: If f′(x)>0 for all x in the interval, then the function f is strictly increasing. If f′(x)<0…

Q: t is the maximum number of people needed to be sure that at most three of them have a birthd th?…

A: We have to find the maximum number of people.

Q: Write a formula for fogoh, where f(x)=√√x+2, g(x)= x+4 and h(x): (fogoh)(x) = (Type an exact answer,…

A:

Q: The table gives the coal consumption of a country for selected years. Use the table to answer parts…

A:

Q: If an converges, then Σa, converges. n=1 n=1

A:

Q: Prove the Cayley-Hamilton Theorem, which says that any square matrix satisfies its characteristic…

A:

Q: Write me A Gr 12 Calcus & Vectors Qestion and Provide the solution (FUll Steps)  that Focuses on…

A: Here, we need to make a question corresponding to calculus and vectors that focuses on rate of…

Q: 1 6 cos 4x = 8 (Cos" α - Cosx) + For each part, calculating the values of the lette identity is…

A: Identity :

Q: A collection of 226 coins consisting of pennies, dimes, and quarters has a value of $16.60. Five…

A:

Q: Use separation of variables with 2 = 45 to find a product solution to the following partial…

A: Partial differential equation is                                   ...........(1)with  .we will…

Q: Show your work neatly and in order. Your explanations should be clear and to the oint. 1. Let W be…

A: The given vectors are .To Prove: is an orthogonal set.To Write: y as the sum of a vector in W and a…

Q: If hyperbola x² 1² + 6² hyperbola. = x² y b² a² 1, then find the eccentricities of ellipse and - = 1…

A: Given that if hyperbola  passes through the foci of ellipse ,then we have to find the…

Q: A Toeplitz matrix is a matrix in which each diagonal (from upper left to lower right) is constant.…

A:

Q: a) Find the real and the imaginary parts of the following complex numbers b) (1 - i)eix/2 c) |ex/4…

A: let,

Q: Solve the initial value problem. dy 5x -x-3 (x + 1)(y + 1)' dx y(1) = 1 The solution is (Type an…

A:

Q: Find the general real solution of this system of differential equations x' y' = x 2y 2x + y =

A: Given that be the two system of Differential equations.NowHere

Q: (z + 3) (2². (a) Find the partial fraction decomposition of f. (b) Find the Laurent series expansion…

A:

Q: X 2 11 у"-3 ху +3y= С Ex

A:

Q: e the given initial-value problem by finding, as in Example 4 of Section 2.4, an (x² + y² = 7) dx =…

A: Given differential equationA differential equation of the formMdx+Ndy=0 is called exact if and…

Q: Consider the contour map below. (a) Sketch and label the following contour plots f (2x, y) f(x, 2y)…

A: Consider the contour map (refer the question).a) To Sketch and label the following contour plots ,…

Q: Find the non-isomorphic abelian groups of  order 360.

A: We have to find the non -isomorphic abelian group of order 360.

Q: With aging, body fat increases and muscle mass declines. The graph to the right shows the percent…

A:

Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y + 13 V₂ = 1 6 The closest…

A:

Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure limit of -5 over the…

A:

Q: At each of the points (20, 2), (3, -6). (.), evaluate the function h(x, y) = y) = √x-y² or indicate…

A:

Q: Find the Laplace transform F(s) = C{f(t)} of the function f(t)--8-9 sin(at) defined for t20. help…

A:

Q: Solve the following initial value problem for y(t) using the method of Laplace transforms to find…

A:

Q: Find lim R→∞ -R ex/6 e + 1 dx using the rectangular contour (explain in detail)

A:

Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake​ Beach, using 1400…

A:

Q: A plastic drinking cup is cylindrical in shape, with an open top. It is required to hold 300 cm³ of…

A: The solution of above question in step by step format is as follows

Q: Solve the equation yzyy-Zy = 2x

A: The  given equation is  Suppose  that Then,from(1), we get,…

Q: Let T: P2 P3 be the linear transformation defined by 3x T (p(x)) = (x + 1)p(x) + p' (1) + 2p(1) dt.…

A: