A tank contains 210 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t. dA dt Find the number A(t) of grams of salt in the tank at time t. A(t) = 9

Q: 1. Consider the function f(x) = -1 0 1 f(x + 4) -2 <x<-1 -1 ≤ x ≤ 1 1 < x≤2

A:

Q: f(x) = x²+6x+5 2-1

A:

Q: A laptob was bought at canadian $770.if the tax of 20% and 13% vat should be paid ,find the least…

A: y% of a number is defined as y100 x number Selling prize id the price at which the item is sold to…

Q: 3 co ós co -6 -3 144 -4 Let y = ,V1= 5 -1 Compute the distance d from y to the subspace of R4…

A:

Q: Let R be the region in the first quadrant that is enclosed by y = f(z) (or z = g(y)) and y = z as…

A: Arc length of a curve y=f(x)  where a≤x≤b L=∫ab1+dydx2dx

Q: Consider polynomials with degree less than or equal to n. We can think that each polynomial…

A:

Q: 8. What rule should be used in deriving f(x) = x³? A. Constant rule B. Sum rule 9. Find dy/dx y=e³x…

A:

Q: Is this matrix invertible ? Explain 9 0 9 0 0 0 0 3 0 0 0 1

A: Introduction: For a square matrix A, if the existence of another square matrix B is confirmed so…

Q: Q3) Consider the initial-value problem dx=y-x,y(0) = 0.5 Use Euler's method with h= 0.1 to obtain an…

A:

Q: 6. Evaluate the inverse z-transform of x(z)= 2z-1 (1-2z-1)2

A: Given: xz=2z-11-2z-12 To find: Inverse z-transform of given function.

Q: what is the difference between Binet's formula to its simplified version? Are there any rules on…

A:

Q: 12 or younger 13 or older Total Signed waiver 10 8 18 Did not sign waiver 20 12 32 Total 30 20 50

A: Let A and B are two events, then;  P(A∪B)=P(A)+P(B)-P(A∩B)

Q: Consider polynomials with degree less than or equal to n. We can think that each polynomial…

A:

Q: 1) Given the function f(x)=- 4x-12 2x+4 determine: (i) the domain (ii) the x and y-intercepts (iii)…

A:

Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. What is the point on…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z)…

Q: 3. Find the Fourier transform of of 1/(1+t²).

A: Let  g(t)=e-at Then g^f=∫-∞∞e-ate-2πiftdt      =∫-∞0e-ate-2πiftdt + ∫0∞e-ate-2πiftdt…

Q: Q2 Solve the ODE y' = 3 x³ – 4y Using Runge- - Kutta 2nd order Method for xo= 0, yo=1, Xn=2 x₂=2 ,…

A: We have to use the second order Runge Kutta method to find the value of y at x=2. It is given that…

Q: The particular solution of the differential equation y" + 2y′ − 3y = 5e²x (Select one) a) yp = e²x…

A: Here we can use operator method to find the particular solution of the differential equation. In…

Q: Let (-3, 8) be a point on the terminal side of 0. Find the exact values of sin 0, csc0, and cot 0.

A: Here we use basic trigonometry to solve this

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

A: The function f(x)=logx is defined for x&gt;0 The function f(x)=x is defined for x≥0 Note: If logba=c…

Q: a¹y¹2'dadydz, where V is the (6) Using suitable transformations, evaluate closed region in the first…

A: Given the integral  ∫∫∫Vx4y4z4dxdydz Where V is the closed region in the first octant bounded by the…

Q: Find the general solution of the PDE. The solution u is a function of x and y. Uxz = x - yz + y²

A:

Q: Task 2: Triple Integral Given a solid bounded by the paraboloid z = 16-1²-y² in the first octant.…

A: Given: z=16-x2-y2 To find: Volume

Q: 03 // A)) Find the volume of solid below? =Y+X x² + 3² AC D4

A: Given solid is

Q: 5. Evaluate the following integral [² 2x cos² x dx by using Trapezoidal's rule with 6 subintervals.…

A:

Q: blem 5. Let P, be the vector space of all polynomials of degree 2 or less, and let H be the subspace…

A: Find the dimension of the subspace we need to determine the number of independent vectors given in…

Q: 1 It is given that p(x) = x³ + ax² + bx-48. When p(x) is divided by x-3 the remainder is 6. Given…

A:

Q: Find r'(t). cos 4 cos³(t)i + 2 sin³ (t)j + k r(t) = 4

A:

Q: Bertrand is a worker in Canada with a continuous income stream at the rate of 650e dollars per year.…

A: Given: 650et To find: 1) Discount rate 2) Nominal interest rate

Q: Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x +…

A: In mathematics, differentiation is the process of determining the derivative, or rate of change, of…

Q: Advanced Math Solve the first order linear differential equation 2' + (2/x)z = 1/2x^-1/2

A:

Q: ne blanks and b = -2x+9y, write

A: Given: a⇀=3x⇀-5y⇀ and b⇀=-2x⇀+9y⇀ We should write the given vector5a⇀-8b⇀in terms of x⇀ and y⇀

Q: Find the Maclaurin series for f(x) = ex+x² using the familiar series. Then use the results to…

A:

Q: 5:2 Find the 2-transform of the sequence x(n)=-duc-m-1) and draw Zero - pole diagram with…

A:

Q: A skydiver weighing 299 lbf (including equipment) falls vertically downward from an altitude of 4000…

A: Use the following formulae, to obtain the solution. Velocity, v=dxdtAcceleration, a=dvdtForce, F=ma…

Q: Solve 4 sin ¹ (7x) X || 2 for the four smallest positive solutions

A: To solve the given equation we shall use the formula                                     sin θ=sin…

Q: Which of the following is a TRUE statement? O A. Jefferson's method of apportionment is not biased…

A: Jefferson's method of apportionment gives exact result.

Q: Let f be a mapping from [1,+∞[ to [1,+∞[, defined by f(x)=x+1/x. Then f is continuous but it is not…

A: A function is homeomorphic when it follows the bijection. The bijective property is one of the…

Q: Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x +…

A:

Q: Q1: Determine whether f(x)= [0,1]. √xsin().if x=0 0.if x=0 is of bounded variation on

A: Given :   f(x) = xsin1x,if x≠00if x=0 To find : Whether f(x) is of bounded variation on [0, 1].

Q: Solve the given initial-value problem. x(x + 1). + xy = 1, y(e) = = 1 dx y(x) = Give the largest…

A:

Q: the centroid z of the frustum of the right-circular cone.

A: The diagram is given as,

Q: Find the particular solution for the given problem. y + 2 = 10x³e², y(1) = 187.02 NOTE: Round the…

A:

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: Given: The population of a community is known to increase at a rate proportional to the number of…

Q: 10. Using 5x5 grids, determine the equation for steady state temperature distribution at T21, T22…

A: Using calculator for solving of system of linear equations

Q: Let D = {x² + y² ≤9, x² + y²-5 ≤z ≤ T= {0 ≤p ≤ 3, 0 ≤0 ≤ 2π, n

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: X = 1 + 6t y = 2 + 4t, ter z = 2t A line is defined by the parametric equation L : If the point (a,…

A:

Q: (a) Find the chromatic number for the graphs A, B, C, D, G, and H: 6 9 A B (b) Classify all graphs…

A: Let GV,E be a graph with vertex set V and edge set E. Assign exactly one color to each vertex of the…

Q: 5. Determine all eigenvalues and eigenvectors of the matrix 000 M = 0 14 0 4 1 Explain your working.

A: Definition: An non-zero vector v is said to be an eigenvector of the matrix A if there exists a…

Q: 3-) (58+2) 32-8 (+2) (8+1

A: