A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.2 gallons. What is the average rate of flow of the gasoline into the gas tank?

Q: Determine if each of the following vector fields is the gradient of a function f(x, y). If so, find…

A: WE can determine if each of the following vector field is the gradient of a function f(x,y) .

Q: 12. 14. Ss sir 1

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Q: Let Ġ(x, y) = (x², y). Calculate the flux of G across the line segment from (0, 0) to (1, − 2).

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A: The given differential equation is:y'''-y'=sin(3x)

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A: Note : As per our guidelines , we can solve first question . Please repost remaining question .

Q: The table below shows the six basic solutions to the following e-system. 2x₁ + 3x₂ +5₁ = 18 4x₁+3x2…

A: Solution : From the given table it is clear that the pairs of (x1, x2) are

Q: 4) Consider the function F(x) = f f (t) dt . Find F¹ (7). O F(7)-F(2) O f(x) O f(7) Of(7)-f(2)

A: Given query is to find indicated derivative.

Q: 2. Use Euler's method to approximate the first three steps of a ten-step approximation to dy 2x+1…

A: Use Euler's method to approximate the first three steps of a ten-step approximation to the solution…

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Q: 2. Convert the following standard a. (y + 1)² = -2(x + 2)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: If t = 3' a) sin t 1. 39463NT 2.0 3. 5. 7. 6. None of these 1 √2 005 (part 2 of 3) 1 1.1 2. 2936 co…

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Q: If the population of an ant colony in 3 days is known to be 2000 and P'(0) 2. What is the…

A: For Linear Growth we have formula, Pt=P0+ktWhere Pt is population at t days.P0 is initial…

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Q: Evaluate the following integral in spherical coordinates. 2 /4 4 csco 2 SS S p² sin o dp do de Ο π/6…

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Q: Nonhomogeneous Linear Equations In this section we learn how to solve second-order nonhomogeneous…

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Q: Find the second partial derivatives of the function f(x, y) = x³y³ + 2x³y. 02f მ2 1. 2. 3. 4. - მ2f…

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Q: By natural increase, a city, whose population is 40,000, will double in 50 years. There is a net…

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Q: 6 S(2 − |x + 4|) dx 3

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Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: If 0 satisfies the inequalities sin (0) > 0, sin(0) cos(0) > 0, in which quadrant must lie? 1.…

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Q: Let y = 3x² + 4x + 2. Find the differential dy when x = 5 and dx Find the differential dy when x = 5…

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Q: Which of the following is equivalent to 2x + 5 S (2-4x) 5 after appropriate algebraic substitution…

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Q: Given the vectors u=-i-3j and w=-7i+5j, find -4u and u-w. Write your answers in the form ai+bj.

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Q: Find the absolute maximum and minimum of f(x, y) = 2x + 4y within the domain x² + y² ≤ 1. Please…

A: Given function:- fx,y=2x+4y Let gx,y=x2+y2-1

Q: 39. y = (cos x)*

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Q: 8) Find a basis for the space spanned by the 5 vectors listed below O T 1 2 26 4 1-1, 1, 0, 1 3…

A: Concept: Reduced roe echelon form abbreviation is (rref) When a matrix is in row echelon form,…

Q: 2. A 71.6m tower is to be constructed on a hill with a slope of 15.6°. Both cables make a 42.5°…

A: We will use sin Rule to find the length of each cable.

Q: options Yart 1. Find Sin(t) part 2. find cos (t) 10 10 options 8 ㅋ 능 None 10 ㅋ 10 8 3. 10 4.…

A: Topic- unit circle WE are given a point on the unit circle as -810,-610we know that on unit circlex…

Q: J.J. Sm 35.) a. cos 210° 36.) a. cos TC 6 DICUS DIJ b. cos 90° b. sin TU 3 C. COS SEU c. sin(-120°)…

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Q: 4 A stone is thrown upwards out of a window, and the rate of change of its height (1 metres) is…

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Q: Problem 2 Consider the function f(x) = x³ 4x² +10. Find the x- coordinates of the local extrema.…

A: We have given function  fx=x3-4x2+10 Derivative of the function is given as  f'x=ddxfx…

Q: answer incorrect

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Q: 7. (a) Let f(x) = 5x5 + x¹ − 2x³ – 1. Explain why f is continuous on (-∞, ∞). (b) Show that f(x) has…

A: We know a polynomial function is continuous in the whole real number plane. If f(x) be a continuous…

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Q: Given the function z = In(x - 2y), find the equation of the tangent plane when (x, y) = (3, 1) in…

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Q: 1. Evaluate the following integrals: b. I sin(4x) cos² (3x) dx

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Q: Find the slope of the following lines.

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Q: Apply the Second-Derivative Test to find all relative extrema of the function  f(x)=cosx-x ,…

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Q: could you please show the solution cleaerly ?

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Q: Let y differentials to estimate Ay = 5x² + 6x + 4. If Ax Ay ~ = 0.1 at x = 1, use

A: The objective of the question is evaluate the "∆y".

Q: 34. S₁ x sin x cos x dx

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Q: Give one example to illustrate that vectors satisfy the triangle inequality. Justify your answer

A: Vectors of Triangle Inequality : u+ v≤u + v

Q: 2. (Section 17.2) Integrate f(x, y, z)=x²-3y + z over the line segment from (3,2, -1) to (0, 1, 1).…

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Q: 11. If g(x) = 4x In x, find g'(x) A. 1+ lnx* C. 4+ lnx¹ B. +4 lnx D.

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Q: Find the curvature by using the formula k(t) = (a) r(t) = (e¹²¹)i +213 +4k at the point where t = 0…

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Q: Use linear approximation, i.e. the tangent line, to approximate 1.86 as follows: Let f(x) =X f(x) at…

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Q: dy (y-1)√y²-2y-3 S.

A: