4) A tank contains 100 gallons of pure water. A brine solution with 1kg/gal of salt enters at 4gal/min, and the well stirred mixture leaves at the rate of 3 gal/min. Determine the amount of salt in the tank after 45 minutes.

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Q: 20. Stan² x dx

A: Consider the integral  ∫tan2x dx

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A: Follow the procedure given below.

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Q: If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then…

A: The volume of the water remaining in the tank after t minutes V=50001-t402  gallons

Q: webassign.net/web/Student Assign 10 5 (6,0) (11, 0) -5F (a) Find the length of each side of the…

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Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

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Q: dr Suppose dx dt dy 4, = 3. Find given that r = dt dt x = 8 y = 2 Write your answer in exact form,…

A: Topic = Derivative

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: (e) If f and g are differentiable then, d -f(g(x)) = f'(g(x))g'(x) dx True False

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Q: 12. Setan 2x sec² 2x dx

A: As per guidelines we can solve only one questions at a time, so if you need more answers kindly…

Q: . Find the area bounded by the given curves. y = 9x² and the x - axis.

A: First we find point of intersection of curve y=9-x2 and x-axis. Put y=0, 0=9-x2 x2 =9 x=±3 Therefore…

Q: 2. The 2 vectors 4â + 3b and â - 2b are perpendicular. Find the angle between â and b if they are…

A: Given :two vectors :4a^+3b^a^-2b^they are perpendicular

Q: 3. Find the equation/s of the TL to 9x² +16y² = 52 which is parallel to the line 9x-8y = 1.

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Q: Question 2. Evaluate the following integral ² 2 0 C. C z² dz dy dx. Show all your work!

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Q: 9. Find f(x) and g(x) so the function can be expressed as y = f(g(x)). 8 y = +4 2 X

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Q: Q4) If the power series method was used to solve the following ODE. (x-0.5)y"-y' + (x² - 1) y=0, x=…

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Q: A manufacturer has modeled its yearly production function P (the monetary value of its entire…

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Q: Given an acceleration function a(t)=, find velocity and position functions, given that v(0)= and…

A: We have to find solutions

Q: # Determine whether the function z = f(x, y) = (why or why not) for for (x, y) = (0,0) (x, y) =…

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Q: ?What is order of the equation (y"+2y+3=0) Second order O First order O Zero order O Third order O

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Q: 2. A 6-ft tall man is walking away from a 15-ft post at a rate of 5 ft/sec in a straight line. How…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Which of the following is a vector quantity ? a) Volume b) Length Oc) Area d) Weight

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Q: A while than 15t 7-47 / र

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Q: Question 4 (a) Solve the following: √4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: Evaluate the following improper integral or state that it is divergent. * 2 3 dz 6 -1 $4 – 2z

A: ∫-1234-2z6 dz Note:     Multiple questions are given, we are answer with only one question. If you…

Q: Find the cross product u x 7 where u úxv- 71 +5j +k and 7 (5,- 4,7).

A: This question can be solved using the concept of cross product of vectors.

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 8 sin(t). The initial…

A:

Q: Suppose f(x) = 3x² + x - 3x²+x-6. Compute the following: A.) ƒ( − 4) + ƒ(1) = = B.) f(-4)-f(1) =

A: Given f(x)=3x2+x-6f(-4)=3(-4)2+(-4)-6=3(16)-4-6=48-10∴f(-4)=38

Q: Given z=x²y+3xy4, x=sin(2t), y=cos(t), find dz/dt when t=0

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Q: Suppose you have a 1024 mg sample of a substance known to have a half-life of 50 years. Find the…

A: Given half-life of sample=50 yrs and the initial sample is = 1024mg.

Q: Q9) The linear form of nonlinear ODE y' - 2y = 2y, is: b) u' - 6u = -6 a) u' + 6u =-6 c) u' - 6u = 6…

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Q: 2) Find the equation of the tangent to f(z) = 3re² when x = 1

A: A detailed solution is given below.

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

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Q: ng the problem) an interval in which the solution of the given initial value proble (t-4)y' + (Int)y…

A: We have to find the interval of t

Q: 5) An isotope of lead decays according to the function remaining, in grams, after t minutes. a) What…

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Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized?

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Q: cos(etan 3x) y cos

A: The given function y=cosetan3x

Q: A coffee merchant sells three blends of coffee. A bag of the house blend contains 100 grams of…

A: This question can be solved using the concept of system of linear equation.

Q: 16. √(16-9x²) dx 17. dx/ (9x² + 4) 18. sin³ x cos x dx 19. f (secs x) dx/csc x 20. Stan² x dx

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Q: Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral…

A: To approximate the given integral using the following rules.

Q: Find the rate of change in the area (A) of a circle with respect to its radius (r) when r = 9. 9TT…

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Q: Find the point at which the line x(t) y(t) z(t) - 5+ 5t -6-8t intersects the z plane. - 7+8t

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Q: .) Find the limit or show that it does not exist. lim √25t²+2-5t 1-x

A: