Oil flows into a tank according to the rate F(t)= and at the same time empties 1+t out at the rate E(t) = n(t+7), with both F(t) and E(t) measured in gallons per minute. t+2 How much oil, to the nearest gallon, is in the tank at time t = 12 minutes. You must show your setup but can use your calculator for all evaluations.

Q: 6. By using the power method, the smallest eigenvalue A of the nonsingular matrix B equal to…

A: Answer is 'False'.

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Given : x'=1-40-201006-12-1-60-40-1x  ; x1=e-t1001  ; x2=e-t0010  ; x3=et010-2 ; x4=et 1030 (a) To…

Q: 03/: Find the area over the region R that lies inside the cardioid r=1+cose and outside the circle…

A:

Q: Transform the below system into the simpler upper triangular form? a11x1 + a12x2 +. . .   + a1nxn =…

A: Given system is a11x1+a12x2+...+a1nxn=b1a21x1+a22x2+...+a2nxn=b2⋮an1x1+an2x2+...+annxn=bn Using…

Q: 8. One card is randomly drawn from a deck of cards. Let, A: The card is a face card (Jack, Queen or…

A:

Q: Problem 4.2_14 (a) Assuming continuity of all partial derivatives, show that V x (V x F) = V(V.F) -…

A:

Q: Q5/: Find the general solution of non-homogenous differential equation using Variation of Parameters…

A:

Q: g(x)=e+1 2 e'e'g(t) dt 0

A:

Q: Find the differential equations of the following primitives by eliminating the arbitrary constants.…

A:

Q: -.) t(3t-2)4 et

A:

Q: Find the differential equations of the following primitives by eliminating the arbitrary constants.…

A:

Q: Show that M indeed is a reflection. To do this, you need to find a (nonzero) column vector v such…

A:

Q: (2 2.) If f(x) = 2x 1 and p(x) cos (x). Find x, for 0≤x≤ 2π, if (f op)(x) = -2

A: Hi! Thank you for your question.As per guidelines we can solve one question at a time in case of…

Q: PLEASE SOLVE IN DIGITSL FORMAT 2. Calculate the following double integrals and draw the region of…

A: Sol:-   ∫12∫17-3y212y-3y2dxdyFirst evaluate ∫17-3y212y-3y2dxIntegral of a constant:…

Q: Angle of a line with the positive direction of the x-axis is 8 (8 is a cute). The line is rotated…

A:

Q: First-Order Equations. The series methods discussed in this section are directly applicable to the…

A: Consider the given differential equation, y'-xy=0 Let us consider that, y=∑n=0∞anxn Then,…

Q: 5. Find the general solution of the differential equation. 21xy' + y = 462X

A: What is Ordinary Differential Equation: Solving an ordinary differential equation is an application…

Q: Q3A) Using Cauchy Riemann equations show that: f(z) = 2z8z5 + 4z6 4z38z² + 2z is analytic in…

A:

Q: Q6] What are the Fourier transforms of these two parts of the pulse? IGO|| arg|G()|| 1.0 0 27 اده 2…

A:

Q: A method sometimes used by pediatricians to calculate the dosage of medicine for children is based…

A:

Q: Name sets with cardinality (a) 365, (b) 12, (c) 7, (d) 11.5, (e) 0, (f) 1024.  

A: Given: The cardinalities, (a) 365, (b) 12, (c) 7, (d) 11.5, (e) 0, (f) 1024. To name: The sets with…

Q: Calculate the circulation of A = p cos ap + z sin o az around the edge L of the wedge defined by 0 ≤…

A: Yes , we can solve using stokes theorem. Note that all the cases z = 0

Q: Investigate the relationship of Fibonacci numbers with the Golder ratio. 1,1, 2, 3, 5, 8, 13, 21,…

A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Estimate the volume of the following solids by Riemann sums m n V=f(x, yj) AA ~ΣΣ i=1 i=1 Estimate…

A: The Riemann sum to find the volume of the area under f(x,y) over the region [a,b]*[c,d] is…

Q: 1- Given the waveform in Figure below, determine if the trigonometric Fourier coefficient has zero…

A:

Q: y′= 2x/1+2y, y(2)=0 Find an explicit solution for the initial value problem. Plot the graph…

A: Differential equation

Q: Q1:/Verify that the given function is harmonic and find it is harmonic conjugates so that f(z) = u +…

A: Harmonic conjugate of the function so that function is analytic

Q: We form the intersection of two sets. We know that one of them has n elements and the other has m…

A: Given : A=n , B=m To Find : Cardinality of A∩B

Q: ILLUSTRATION 1.10 Using distance formula, prove the Apollonius' theorem that is in AABC, AB2+ AC² =…

A: What is Apollonius Theorem: The line segment that joins a triangle's vertex to the middle of its…

Q: Let f(x)= Ax² + Bx + C where A, B and C are real numbers. Prove that if f(x) is an integer whenever…

A:

Q: Q2) Find $dz 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using…

A: What is Complex Integration: Like a real valued function, a complex valued function can also be…

Q: Compute 1₁ sin (y)dA where D is the region bounded by z = 0, y = 1, and y = √a. 2

A:

Q: In the following implicit solution, use the initial condition y(1) = −3 to find C y³ - 5y = 4x - x²…

A: Introduction: To identify a specific solution, we typically need initial circumstances or additional…

Q: Q4:A/ By using Exact equation solve the first order differential equation 2y²+ ye+ (4xy + xe +…

A:

Q: A line OP makes equal angle with coordinate axes then find its direction cosines.

A:

Q: 7. Find y' for sin x + sin y = 1. 8. Find y' for xcos y = sin(x + y).

A: Sol

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

A:

Q: Q1:/Verify that the given function is harmonic and find it is harmonic conjugates so that f(z) = u +…

A:

Q: Q4:A/ By using Exact equation solve the first order differential equation 2y² + ye+ (4xy + xe +…

A:

Q: Suppose that ACR is bounded below, and define B = {b € R | b is a lower bound for A}. Prove that sup…

A:

Q: 6. What is the coefficient of the term independent of x and y in the multinomial expansion (5x + ³ +…

A:

Q: Ok so the question says " evaluate. Write your answer as a fraction or whole number without…

A: The negative exponent rule: Tells us that the number with a negative exponent should be put to the…

Q: Develop sin t in the Half-Range cosine series in the interval 0<t<L. L :(0)\ novo ms 10l

A:

Q: The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with…

A:

Q: Find the sum of the degrees of the vertices of each graph in Exercises 1-3 and verify that it equals…

A: We know that, Degree of vertex is the number of edges passing through that vertex. We need to…

Q: 3/2 (1 +i)"

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: 7. The least square curve of the form y = ab* to the following data is (a) y = 3 ex In2 (c) y = 3 e2…

A: Hint: Substitute the given values in the given options and identify the correct one.

Q: 2. If the edge of a cube is 1.75 m, then how many square centimeters are there in its entire…

A: Sol:- Edge of Cube = a = 1.75m Entire surface area = 6a2

Q: 7. Find y' for sin.x+sin y = 1. 8. Find y' for xcos y = sin(x + y).

A:

Q: In the following system Problem, categorize the eigenvalues and eigenvectors of the coefficient…

A: Given system of differential equation is x1'=2x1+3x2x2'=2x1+x2 We can write it in matrix form…