A tank contains 7070 kg of salt and 10001000 L of water. A solution of a concentration 0.035 kg of salt per liter enters a tank at the rate 8 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? (b) Find the amount of salt in the tank after 2.5 hours. (c) Find the concentration of salt in the solution in the tank as time approaches infinity.

Q: 2. Determine if the series n n4 +1 n=1 Σ (-1)³n converges or diverges.

A:

Q: Determine what x = 5 is (max/min/neither) of the function f (x) = 2x2 − 3x + 9

A: Given f (x) = 2x2 − 3x + 9

Q: Find the antiderivative, G(t), of the function g(t) = (3n²t² – tª)V3n² – t². |

A:

Q: 6 Find the circumference of a circle with an area of 95.03 m2.

A:

Q: Find all distinct (real or complex) eigenvalues of A. Then find the basic eigenvectors of A correspo...

A:

Q: 1 8 Find the determinant of [0 -3 7] 1 2 3 4

A:

Q: Graph the feasible region for the follow system of inequalities by drawing a polygon around the feas...

A: 5x+4y≥362x+3y≥18x+y≥8x+y≤9x≥0, y≥0

Q: Consider the differential equation: y" – 6y' + 9y = (x + 1)e³* What is the particular solution Yp = ...

A: We can solve this using given information

Q: 18. Suppose that we were to approximate f (1) = cos æ using the 3rd degree Taylor polynomial T3(x) =...

A: Given suppose that we were approximated f(x) cos(x) using the 3rd degree Taylor polynomial T3x =1-x2...

Q: 4dx + (x -y + 2)²dy = 0 %3D

A:

Q: Visually estimate the location of the centroid of the region shown. Then find the exact coordinates ...

A:

Q: Find the volume of the region bounded by the plane z = -x - 2y + 2, and the planes x = 0, y = 0, and...

A:

Q: 1. Determine if the series cos" (;) en? n=1 is absolutely convergent, conditionally convergent, or d...

A: Root test, for converge

Q: Call a function f :N - N eventually nondecreasing if the set decr(f) {n eN|S(n+1) < f(n)} is finite....

A: The problem is related to calculus and the topic is countability. We have to ask about range of the ...

Q: When gcd(a, b) = 1, prove σ(ab) = σ(a)σ(b) and find σ(200) and σ(720).

A:

Q: A. In the figure below, CE and LA are diameters of ON. Use the figure to answer the following. If mL...

A:

Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

A:

Q: Express the given complex number in rectangular form into polar form. -5 – 5i3 ○ 5/2 [cos(플) + isin(...

A:

Q: Evaluate the moment Mx and My of the region bounded by y = 2x + 1, x + y =7 and x = 8.

A:

Q: Find the particular solution of y' - 2y = e3x if y(0) = -5 using Laplace Transform. %3D %3D

A: The given initial value problem is                                               y'-2y=e3x , y(0)=-5...

Q: 1. Consider the series (-1)"+1 n! (a) Determine if the series is absolutely convergent, conditionall...

A:

Q: 7(E) - * -5.x +9y 4r - 7y invertible and find a formula for T-, (E) - 13. Т is a linear transformati...

A:

Q: Find the volume of the barn shown below. 20 ft 10 ft '17 ft 15 ft 30 ft

A:

Q: Find the coefficient a, of the Fourier series representation of the function with period T= 1/50 (1,...

A:

Q: Consider the series In(k) k2 a) Enter an integral whose convergence or divergence is equivalent to t...

A:

Q: Use a triple integral to find the volume of the given solid. the solid bounded by the parabolic cyli...

A:

Q: x² + ax - 2bx - 2ab – x - 2ax2 - 2bx2 dx x* + ax² – 2bx2 - 2abx

A:

Q: 29 Sin 6

A:

Q: Evaluate using Wallis' Formula: So sin® x cos4 x dx -Tt/2

A:

Q: 40. In each of the following, find the 6 X 6 matrix A = [a,] that satisfies the given condition: Si ...

A:

Q: Determine the particular solution 2y" + 5y' + 3y=0; y (0) =3; y' (0) = 2 Options y = -10e-3x/2 - 13e...

A:

Q: Use spherical coordinates. |II (2 – x² – y²) dV, where H is the solid hemisphere x? + y2+ z² s 9, z ...

A:

Q: Prove that the set V of all real valued continuous (differentiable or integrable) functions defined o...

A: We have given that , V is a set of all real valued continuous functions defined on a , b with vector...

Q: A nutritionist is studying the effects of the nutrients folic acid, choline, and inositol. He has th...

A:

Q: Find the length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3/2).

A:

Q: 1. Using a truth table, prove De Morgan's laws as follows. ¬(pVq) = -p ¬q & ¬(p^q) = -pV¬q

A:

Q: a bc de f Given det = 4, find the following determinants. g hi ghi a b c det de f a b c 6d + a 6e + ...

A:

Q: An investor has $80,000 to invest in a CD and a mutual fund. The CD yields 6% and the mutual fund yi...

A:

Q: х* + ах + 2bx + 2ab + 2x3 — ах* + 6bx? dx х4 + аxх3 + 2bx3 + 2abx?

A:

Q: Q1 Solve the following differential equations dy X-y+3 2x -- 2y + 5 dx 1)

A:

Q: Determine the exact simple interest on P 5,000.00 for the period from June 10 2015 to November 21, 2...

A:

Q: Consider the system of linear equations below. Solve for D. 2A - B + 3C - D = 5 A + B - 2D + E = 0 -...

A:  

Q: Consider the differential equation r y" + 5xy + 4y = 0. It is given that I= 0 is a regular singular ...

A:

Q: Consider the following transfer function: F(s) = 25 + 5s? + 3s + 6 B = A + D + s° + 6s? + 11s + 6 S ...

A:

Q: Evaluate the moment Mx and M, of the region bounded by x = 2y – y? and the y=axis.

A: A double integral involves the integration with respect to the product of the variables x and y. The...

Q: -2 4 A = -1 -3 4. -6 Find dimensions of the kernel and image of T() = Ai. %3D dim(Ker(A)) = dim(Im(A...

A:

Q: 4. Solve the equation SHOW YOUR COMPLETE AND CLEAR SOLUTIONS. x² (y')° = 2y² – xyy' -

A:

Q: • Consider the (nonlinear) initial value problem / = -2y, y(0) = yo Does it have a solution for a) y...

A:

Q: Find the Laplace transform of f(t) defined by 2cos(120t + 45°). V2 (s – 120) b) s2 + 14400 V2(s + 12...

A:

Q: Instruction: Solve the following system of homogeneous linear differential equations. Present your s...

A: