A tank initially contains 40 gallons of pure water. A solution with 1 gram of salt per gallon of water is added to the tank at 3 gal/min, and the resulting solution leaves at the same rate. Find the quantity Q(t) of salt in the tank at time t > 0. Hint: Q'(t) = rate of salt in - rate of salt out.

Q: Find one positive root of f (x) = e" – 2x 5 using the Fixed-Point Iteration Method with an initial e...

A: NOTE: According to guideline answer of first question can be given, for other please ask in a differ...

Q: raluate the iterated integral by converting to polar coordinates. 16 – x2 (x2 + y2) dy dx dr de =

A:

Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is...

A:

Q: Question No. 1: Part:a: For matrix -1 4 - 2] A = -3 4 | -3 1 3 Calculate all eigenvalues and eigenve...

A: The given problem is to find the eigenvalues and eigenvectors of the given matrix and also find the ...

Q: 2. Are the following propositions logically equivalent ? p→ (¬q^r), ¬pV¬(r → q). Yes No Don't know 3...

A:

Q: A quiz consists of 8 multiple choice questions, each with 4 options.  In how many ways can a student...

A:

Q: z=√9i solve the complex number in complete solution

A:

Q: 3. Find the area of the surface having parameterisation r(u, v) = (uv, 3uv, v), where u E [-2, 2] an...

A: Surface area of the surface

Q: Let V be a vector space with basis B = {w, x, y, z}. Let S {u1, u2, u3, u4} C V, with u1, u2, U3, U4...

A: Any sub set containing n vectors in n-dimensional vector space may or may not be a basis. Basis of a...

Q: Find the distance between the point and the line given by the set of parametric equations. (Round yo...

A: Given:   The line given by the set of parametric equations. (3, -8, 4); x = 2t, y = t - 3, z = 2t + ...

Q: Show f(x) = x/4 – In(x) is positive for x e R sufficiently large. As well, use the p-series 1 to sho...

A: We have to check whether given series is convergent or divergent.

Q: f(t) = 2Ct -4)

A:

Q: What is Fred deemed to own based on the following of Slate Rock and Gravel, Inc.: Fred owns 30% Fred...

A:

Q: Solve 2 part only in 30 min nd take a thumb up plz

A:

Q: Use the Geometric Series Test to show that 0.3+0.03+0.003 +… converges.

A:

Q: Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 15 5] 5...

A:

Q: Characteristic Equations Q1.Find the general solution of following PDE equation (a) (5x + R)uz + (7x...

A:

Q: Use the field norm to show: a) 1+ 2 is a unit in Z [ 2]

A:

Q: V1-x² 1-x²-y² e-3(x²+y²+z²)² dz dydx a) Evaluate

A:

Q: 3s+9 3. F(s) = s2 +5

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Evaluate the double integral f(r, 0) dA. 2 sin(0) cos(0) dr de Sketch the region R. A/2 T/2 3h 2 1 -...

A: Evaluation of the double Integrals  

Q: In a partially destroyed laboratory record, only the lines of regression of y on z and x on y are av...

A: given , partially laboratory records only the lines of regression of x on y and y on x 4x-5y+33 =0  ...

Q: Solve y (xy + 2x?y) dx +x (xy-xy?) dy = 0.

A:

Q: A periodic function of period 2n is defined for 0 1) u÷- x- 2π ( 5π< x < 2π) Sketch f (x)for (-27 <...

A: Given: Let us consider the given  function, fx=x0≤x≤12π12π12π&lt;x≤π-12ππ&lt;x≤32πx-2π32π≤x≤2π

Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

A:

Q: 3. Given an equation of a circle, determine how to find a point on the circle. Determine how to find...

A: We have to find the point on circle. And equations of tangent line which is passing through that poi...

Q: solve one real root of e* – 2x – 5 = 0 with æo = -2 using the Fixed-Point teration Method until abso...

A:

Q: vitomin B w te n pe e Solution : O let x Ounce of food P. y = Ounces of food Q. This is decision var...

A:

Q: . Solve y – 2px = tan-1 (xp?).

A:

Q: Determine the root (if they exist) at the given interval for the equations as shown: x4 – 28x³ + 288...

A: The given equation is: x4-28 x3+ 288 x2-1116x+1296=0 To find the root of this equation we use Bisect...

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A:

Q: (e– 1)y' = 2 + cos.x -

A: Let us consider the differential equation of the form dydx=f(x)g(y) Rewrite the equation as 1g(y)dy...

Q: Problem 5. Compute the eigenvalues and eigenvectors of 1 X = %3D 1 4

A: Given matrix is X = 12-14

Q: 3.3 hy grephing Solve A. Minimize C =10x +15y s,t. X+y 3x ry Zld ー2x +3y 23 x20, y 20 B. Maximize P=...

A: We have to solve the problems by graphing.

Q: Solve for the Laplace transform : (number 12)

A: Laplace transferom of the function

Q: 6. Write down a matrix A in row echelon form with the following properties: 5 rows, rank(A) =4, null...

A: We want to find a matrix which satisfy given conditions.

Q: Show that if a | b and b | a, where a and b are integers, then a = b or a = −b.

A: We show that if a | b and b | a, where a and b are integers, then a = b or a = −b.

Q: 3 The Transpose of a row matrix is zero matrix diagonal matrix row matrix column matrix 4 If A is a ...

A:

Q: The area of the top of the gift box is Acm'. (a) () Find A in terms of p and q. (1) 192 + 34 + 48. S...

A: Area of a right angle triangle =(1/2)*base*height 

Q: The intercept of a straight line on the x - axis is -3. If (5, 2) is a point on the straight line, t...

A: Given points of straight line are (-3, 0)  and (5, 2)

Q: Use the Geometric Series Test to show that 0.3+0.03+0.003+…… converges.

A:

Q: Problem 4. (a) Define a linear operator on R² by performing the following operations in order: a she...

A: As per our guidelines we are supposed to answer only one question that is the first question. For th...

Q: let (Riae) be aring of real numbar's andf fg Eply R. Such That f= to,,-1,22010-) F-lo-してソの (hoラ-20 )...

A:

Q: dy + 2 dy + y = sinh 3t – 5 cosh 3t ; y (0) = -2, y (0) = 5 II %3D |3D | dt? dt

A:

Q: fx (partial derivatives)

A: We can solve this problem by using complete derivative .

Q: ----j n(x, y) = x² + 3xy – 6y has a critical point at (2,- Use the second derivative test to describ...

A:

Q: i. Find the limit of the following. 4n -2n + 4n 2n +7 n+4 n – 5n+6 a) lim n - 2n 5n -3n b) lim -16 c...

A: We have to find the limit of   e) limn→0nensin n f) limn→32ln(4n-11)n2-9

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula. ...

A: Solution:   This is an equivalence relation since:A U Y = A U YA U Y = B U Y implies that B U Y = A ...

Q: 3. If the following series is convergent, give its sum, showing all work. If it is divergent, write ...

A: Given series is ∑n=1∞ 34n + 5n

Q: -2 -5 8 -17] -5 1 1. Consider A = 1 3 11 -19 7 1 1 7 -13 5 -3 a. Find the basis for, and the dimensi...

A: