A large tank is partially filled with 100 gallons of fluid in which 30 pounds of salt is dissolved. Brine containing pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 40 minutes. (Round your answer to two decimal places.) Ib

Q: 3. Graph and then find the area of the region bounded by the curves y = 8x - x² and y=2x−7.

A:

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

A:

Q: Use the Gaussian elimination to solve the following equations, so the variables X and Y are. ****…

A: Given equations, 8x-4y+4z=12,-6x+3y+3z=9,2x-y-2z=-6

Q: 2. Does the equation x² + y² + z²-3x - y + 3z = 0 represent a sphere? If so, find the center and the…

A:

Q: Problem 1. A rectangular enclosure is to be built next to a river. There will be no fence on the…

A:

Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

A:

Q: 7. Find the volume of the solid generated by revolving about the y axis the area between the first…

A: Concept: According to the shell method, the volume by revolution about the y axis is…

Q: rite the first five terms of the sequence: √n² +10n-n}+1 = etermine whether the sequence converges,…

A:

Q: Calculus I

A: use the table and differentiation to find the correct answer.

Q: c ( # ) **(#) tan (²) sec (²) sec ye 22 (=) sec² x² c¹² ( ² ) ye = dy O None of the choices af dy…

A: To find out the partial derivative.

Q: 1. find the derivative 2x² - 6x³ + 5x²-3x + 17 Enter your answer

A:

Q: The logarithmic equation 2 log c = b, where a > 1, expressed in exponential form could be Oa² = bc…

A: Given

Q: A research lab recorded the decay of a radioactive substance. The data table shows the amount of the…

A:

Q: 1. Determine the value of each of the following limits if they exist. 1²-21-8 +¹ -1 X 3a) lim- b)…

A:

Q: Solve the following. 1. Find the volume generated by revolving the first-quadrant area bounded by…

A:

Q: Your answer is incorrect. Graph the function. y--33 Plot five points on the graph of the function:…

A:

Q: I For what values of x does the graph of f have a horizontal tangent? (Use n as your integer…

A: In this question, we want to know at which points , the function f have horizontal tangent.

Q: How many odd three digit number can be written using the digits 2, 3, 4, 5, and 6?

A:

Q: (C): Find representative Fraction scale (R.F) from verbal statement of (6 inch to 1 mile) (12mile to…

A: 6 inch to 1 mile 12 mile to 1 inch

Q: Perform a first derivative test on the function f(x) = 2x3 + 3x2 - 72x+4; [-4,7]. a. Locate the…

A:

Q: Using the appropriate substitution, what is the homogeneous form of the given ODE. (x - 2y + 4) dx +…

A:

Q: Solve the following initial value problems. (a) 2ut + ur= -2u, z,te R, t> 0; u(x, t) = f(x, t) on…

A:

Q: d- d³y dx3 d²y +6 dx² - Q.2-Solve the differential equation 15 - 100y = 0 dy dx

A:

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

A:

Q: Solve the differential equation. 13. ( sin θ – 2r cos^2 θ) dr + r cos θ ( 2r sin θ + 1) dθ = 0

A:

Q: Given x = 5t - 5 and y = 25 sin t dy da t-0 (ii) dy da 2 t-0

A:

Q: Use the Limit Definition of the Derivative to find f'(x) for the following function. You may NOT use…

A: Use limit definition to solve

Q: D Question 5 If y = 7³/2, then True False dy = ¹/2

A:

Q: dy = y cos(x), Where y(0) dx = : 1.

A:

Q: (b) The graph of y-g(x) is shown. Draw the graph of y=-g(x).

A: we have the graph of F(x) vs x when we put -x in place of x the graph will be mirror across Y- axis…

Q: When the expression log, (47) - log, (3), b > 1, is written in the form log, a, the value of a, to…

A: We need to find a.

Q: Find dy dx for sin(xy) + y³ = x² + 1 and use it to find the equation of the tangent line at the…

A: use differentiation for finding the equation of tangent line.

Q: Find the first partial derivatives of the function. f(x, y) = x6y3 + 4x7y

A:

Q: Determine dy/dx, if the curve is described by the equation 4y^3-5x^2y=4x^2

A:

Q: Problem 2. A cylindrical can without a top is to be made to have volume 100cm³. Find the radius of…

A: We have to use a concept of derivatives

Q: b) Suppose to i that and V х-у Calculate the x and and y by and Jacobian ð (u, v) 2 (x, y) hence…

A: Suppose that x and y are related to u and v by…

Q: Express the number as a ratio of integers. 3.898 3.898898898...

A: 3.898898898..... this can be written as  3.898898898..=3+ 0.898 + 0.000898 + 0.000000898 + .. ...  .…

Q: 9. Find the volume of the solid generated by revolving about the y-axis the region bounded by the…

A:

Q: 2|6x + 4 ≥ 1 OX - 7/12 O-7/12 - 12/7

A:

Q: [C (sec 9x + csc 9x)³ dx

A:

Q: For the function f(x)=x^3-3x+1 defined on the interval -3 ≤x≤3. Find absolute maximum and minimum…

A:

Q: Below is the graph of y=3√x. Translate it to make it the graph of y=3√x-2+4. of x 5

A:

Q: Graph the function. f(x)=√x-2 Plot four points on the graph of the function: the leftmost point and…

A:

Q: 6. 7. 8. (ex + e + x) dx 24t dt [2(5x) dx

A:

Q: Find the general solution of the given ODE. * (x+y-1)dx - (x + y)dy = 0 x+y+ ln |2x + 2y - 1|= C…

A: The given ODE:x+y-1dx-x+ydy=0.We need to solve the above ODE.

Q: 440 All boxes with a square base, an open top, and a volume of 110 ft3 have a surface area given by…

A: Given problem:- All boxes with a square base, an open top, and a volume of 110ft3 have a surface…

Q: 5. find the derivative 2x (7) + 6x (7) - 2x (²) + 210 Enter your answer

A:

Q: 7. Find the volume of the solid generated by revolving about the x-axis the region in the first…

A:

Q: Q1 (a) Using the second shift theorem, find L-1 se s² +91

A: Aaaà

Q: Determine whether the statement is true or false. An equation of the tangent line to the parabola y…

A: