Topic: Differential Equations A tank contains 80 gallons of brine with 5kg of salt. Another brine solution with 2lb/gallon of salt enters at 2gal/min and the mixture leaves at a rate of 4 gal/min. Find the amount of salt in the tank after 10 mins

Q: A rectangular beam is cut from a cylindrical log of radius 15 cm. A cross-section of the log is…

A: The given figure is:   Radius r=15 cm Let the dimeter is d  ∴d=2r=215=30cm

Q: f(x) = 2x³ - 3x² - 36x +14 use f'(x), find decreasing interval

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Q: Find the linearization L(x,y) of the function f(x,y)=²x cos (3y) at the points (0,0) and ¹ (0.7) The…

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Q: Use differentials to estimate the following. Give all answers correct to at least 3 decimal places.…

A: We have to find asked area.

Q: 52 16 59 12 20. If an = 4(3)″−¹, what is S3?

A: Given: an=43n-1

Q: a tank contains 1000L of brine with 15kg of dissolved salt. pure water enters the tank at a rate of…

A: The answer is in step 2.

Q: 2) Find the solution of the system, by hand, without using a matrix, or show that it is…

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Q: 2. Let y = 3x23 a) Find the change in y, Ay when x = 5 and Ax = 0.02. b) Find the differential dy…

A: Given function y = 3x2

Q: Let f be the function defined by f(x) = x - 2 sin(x), 0≤x≤n. On which interval(s) is f increasing?…

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Q: Question 6 of 10, Step 1 of 1 Answer Suppose that y' is proportional to the cube root of .x, and…

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Q: Suppose that f is a function given as f(x) = 3x² - 7x. Simplify the expression f(x + h). f(x + h) =…

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Q: 2 få 8xclx o x4-8x²+32 3. f= 1/4 (1 + sinx) dx + 4. Find y if f (2x+7)dx य (1+ sinx) dx = In/ x² +…

A: (2). The given integral is: ∫02 8xx4-8x2+32dx

Q: If C(t)= 18.5te -0.3t measures the concentration, in of a drug in ng ml' a person's system t hours…

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Q: to find дz Әх дz ду . II = дz дх дz дх ƏF дх дF əz and and дz ду dz ду x2 + 8y2 + 7z2 = 1 - OF ду OF…

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Q: Let H(t) be the cost of heating a building in dollars per hour when the outside temperature is t…

A: Given that Ht be the cost of heating a building in dollars per hour when the outside temperature is…

Q: x  ≤  12 −4x + 144 x  >  12 Evalute 36 ∫ 0 f (x) dx. (Note that since  f (x) is defined in a…

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Q: The slope of the tangent line to the parabola y = 3x² + 3x + 7 at the point (−1, 7) is: The equation…

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Q: Of all rectangles with a perimeter of 30, which one has the maximum area? (Give the dimensions.) The…

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Q: Question 5. The rate of change in revenue from a recently-installed machine is 60,000t + 45,000…

A: The rate of change in revenue from a recently-installed machine is  60,000t+45,000 dollars per year…

Q: Exact differential Equation    M(x,y)dx + N(x,y)dy =0 ∂M/∂y = ∂N/∂x   solve the following…

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Q: metal Bar at a temperature of 120°F is placed in room temperature 10F, If after 20 mins, the…

A: Given: T1=temperature of the metal bar, 120°FT2=room temperature, 10°FT=temperature of the metal bar…

Q: In a scale model of a table, 1 centimeter represents 6 inches. Answer the following. Scale 1 cm: 6…

A: Given that:- Scale 1 cm:6 in

Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

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Q: dy Find by implicit differentiation. dx dy dx 9x2 + y2 = 9

A: Differentiation

Q: S²2 Sex+257 ² cos(3y² – 1³) dydx 2

A: The given integral is:∫-22∫x+22x+2 cos3y2-y3 dy dx

Q: The equation of the tangent line to a function fatxa is given by the equation y = 12(x-a)+b. Use…

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Q: Find the volume of the solid enclosed by the surfaces z = 8 - 2(x² + y²) and z = 6√x² + y²

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Q: Obtain the particular solution satisfying the initial conditions indicated. 2. (t² − x)dt – tdx = 0;…

A: We need to solve D.E.

Q: At time t=0, a particle is located at the point (9,1,6). It travels in a straight line to the point…

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Q: | dy dx sin √√x √y

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Q: The distance that a free falling object falls is directly proportional to the square of the time it…

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Q: Consider the function f(t) = 4 sec²(t) — 8t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: en: y = u² - 2u¹ and u = x + √x. Find when x = 9.

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Q: Let 21 and 22 be complex numbers. In particular, let z₁ = a + bi and 22 = c + di, where a, b, c, d…

A: Given: z1=a+biz2=c+di   We are required to prove a. z1+z2=z1+z2b. z1.z2=z1.z2

Q: Sketch the region that corresponds to the given inequalities. 2x - y ≤ 9 x + 2y s7 -10 O -5 y 10 5 5…

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Q: You want to build a 1200 square foot rectangular infinity pool. Three of the sides will have regular…

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Q: Evaluate the integral. S² (6ti - t³j+ 2t³k) dt

A: B=∫02(6ti-t3j+2t3k)dt∫tndt=tn+1n+1+c

Q: = 10: Consider the helix r(t) = (cos(8t), sin(8t), -1t). Compute, at t =

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Q: Find the scalar equation of the plane containing the line: l1: [x, y, z] 1₂: [x, y, z] - [2, 6, -1]+…

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Q: For the following function, a) give the coordinates of any critical points and classify each point…

A: As per the bartleby guidelines for question having multiple subpart question expert must have answer…

Q: (c) Now find the exact values of a and b that satisfy the conditions in part (a).

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Q: Obtain the general solution of the following differential equations. 5. xydx-(x+3y²)dy = 0 Ans.…

A: The given differential equation is: xy dx-x2+3y2dy=0

Q: In the third to last line why are is 2cos phil multiplied by 1/2

A: We need to explain the reason behind doing the below step:

Q: Let f(x) = 4x² + 13x - 3. ƒ(x + h) − f (x) Using the definition of derivative, f'(x) =lim h→0 h…

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Q: The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's…

A: The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's…

Q: Express the volume of the solid enclosed by the paraboloids y = 3x² + 3z² and y = 5-2x²-2z² with a…

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Q: For the given cost function C(x) = 19600 + 400x + x² find: a) The marginal cost function = b) The…

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Q: If   C(t)=55te−0.1t measures the​ concentration, in ngml​, of a drug in a​ person's system t hours…

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Q: = a tank contain 100 gallons of the pure water, a Brine solution w/ 41b/gall OF salt enters at 4 gal…

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Q: Which of the functions are polynomial functions? (Select all that apply.) > > S 13 33 J U C P e 2…

A: To determine the functions that are polynomial functions.