Problem 2 Find the area of the part of the plane 2x + 3y - 4z + 5 = 0 that lies above the rectangle [1, 2] x [3,4].

Q: Sand falls from a hopper at a rate of 0.3 cubic meters per hour and forms a conical pile beneath.…

A: dVdt=0.3 m3/hrr=h2  Where r is the radius of the cone and h is the height of the cone

Q: Find //24. a Round your answer to four decimal places. -dA, R= [0, 1] x [-4,4]

A: ∬xy2x2 + 1dA0 ≤ x ≤  -41 ≤ y ≤  4

Q: Minimizing Construction Costs The management of the UNICO department store has decided to enclose an…

A: Total Area = 827 ft2 Cost of pine board fencing = $7/running foot Cost of Steel fencing = $2/running…

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: On doing differentiation of the given function and will put equal to zero we will find the critical…

Q: Find Vz. 7xe³y x + 3y NOTE: Give your answer in unit vector notation; that is, in terms of i and j.…

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Q: Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. Absolute…

A: The function f that is continuous on interval [1, 5] Absolute maximum at 5, Absolute minimum at 2,…

Q: 1. Find the absolute maximum and minimum values of the func- tion f(x, y) = x² + y² − 3x − xy on the…

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Q: Find Vz. 2x + 5y 2x - 5y NOTE: Give your answer in unit vector notation; that is, in terms of i and…

A: z=2x+5y2x-5y

Q: 2. How do you compute the amplitude of a graph that has a minimum and maximum value of y? What is…

A: The amplitude of y=asin(x) and y=acos(x) represents half the distance between the maximum and…

Q: 5. Write the equation of the ellipse given that the co-vertices are (-13,7), and (-3,7); and the…

A: Given: The co-vertices of ellipse are (-13,7) and (-3,7).Length of major axis=16   We are required…

Q: Find the time it takes for $7,600 to double when invested at an annual interest rate of 9%,…

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Q: Graph the equation: S(x)=3^x-2

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Q: Which of the following is true of 4*(x-410 dx? Select the correct answer below: 1 -9(10)⁹. The…

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Q: Find a function f whose graph is a parabola with the given vertex and that passes through the given…

A: given vertex is (1,-1)passing througt point (2,3)standard form of parabola is y=a(x-h)2+k where…

Q: 1. a) Copy and complete the table below: Original Function First derivative Second Derivative y =…

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Q: 4. Find the equation of the tangent line to f(x) = ln x at x = 1. Then use the equation of the…

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Q: The graph of a 5th degree polynomial is shown below. Use it to answer the questions. y, -1 Al N (a)…

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Q: How many strings of length 12 of uppercase letters contain exactly three vowels? Note: vowels and…

A: How many strings of length 12 of uppercase letters contain exactly three vowels? Note: vowels and…

Q: Find the directional derivative of f at P in the direction of a. f(x, y) = tan-¹(²); P(-2,2); a=−10i…

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Q: Evaluate A) 3 (x-9) ² 8 converges B) converges c) converges (e D) diverges 9/h O dx

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Q: A trough is 7 meters long, 2 meters wide, and 1 meters deep. The vertical cross-section of the…

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Q: Find the directional derivative of fat P in the direction f(x, y) = 3x³y¹; P (5, 1); a = 7 i − 24 j

A: given function is :-f(x,y)=3x3y4point  P(5,1) and  a = 7i-24jthen we have to find directional…

Q: B. Let f(x) be an odd, differentiable function. This means that f(x)= -f(-x) We know that f'(x)= O…

A: Let f(x) be an odd, differentiable function this means that f(−x)=-f(x)

Q: 7t - 7t² -t+3' 7t2-7' -3t³ +6, -1 Let F(t) = (-773 Find '(t) 7' (t) = ( (..) Question Help: Video…

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Q: A train is traveling 50 km per hour along a straight track, moving in the direction as shown in the…

A: We use Pythagoras theorem and differentiation to get a solution for this question.

Q: Find the only possible solution to the nonlinear programming problem max (200 - 9x² - 72²) subject…

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Q: -0.00012097t The amount of carbon-14 present in animal bones t years after the animal's death is…

A: the amount of carbon-14 present in animal bones t years after the animals death is given by…

Q: Suppose that f(x, y) = 1 at which {(x, y) | -4 ≤ x, y ≤ 4}. Q Then the double integral of f(x, y)…

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Q: K Suppose the average daily metabolic rate for certain types of animals can be where m is the mass…

A: The solution is shown in step-2

Q: Find a) any critical values and b) any relative extrema. g(x)=x²-3x+7

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Q: Find a unit vector in the direction in which f(x, y) = 8 - x² - y² decreases most rapidly at…

A: The direction in which the function  f(x,y)=8-x2-y2 is decrease is -∇f(x,y) .

Q: ← For a certain product, cost C and revenue R are given as follows, where x is the number of units…

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Q: Find Vz. 4x 1 (42²) NOTE: Give your answer in unit vector notation; that is, in terms of i and j. 16…

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Q: y=0 www 17

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Q: Find the critical numbers of the function. f(x) = x³ + 3x² − 9x (smaller value) (larger value) X X…

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Q: Find the number of units that must be produced and sold in order to yield the maximum profit, given…

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Q: 6 Find ₂- dx. 2 (x-3) 5 Select the correct answer below: The integral converges to 12. The integral…

A: ∫246x-325dx

Q: A nonhomogeneous equation and a particular solution are given. Find a general solution for the…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Given :fx, y=xyP2,8 formula used :Duf=∇fx, y·u→

Q: A rescued whale is released into the ocean 400 meters due east of a coast guard station. The whale…

A: I am attaching an image so that you understand each and every step.

Q: (a) f(x) f'(x) = (b) y dy dt = X -4e¹0t √1-1⁹ 25

A: Here we will use quotient rule and product rule of the differentiation to find the differentiation…

Q: Evaluate 10 3 (x-9)6 dx. Select the correct answer below: 6 5 O The integral converges to O The…

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Q: Your calculator can be used to directly estimate definite integrals. (See the calculator tutorial.)…

A: The given integral is x5, limit from 2 to 5.

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: Solve the following system of equations using Gaussian elimination or Gauss-Jordan elimination. -2x…

A: Given system of equations -2x - 9y - z = 18 -4x - 6y - 2z = 12 3x + 9y + z = -17

Q: Use the Laplace transform to solve the following initial value problem: y" + 7y' = 0 y(0) = −2,…

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Q: Given that Vf(2, -13) = 2i- j, find the directional derivative of the function f at the point (2,…

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Q: A hemispherical bowl of radius 11 cm contains water to a depth of h cm as shown below. (a) Find the…

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Q: (87) ban 13. Let rr, be vectors in R", and let Q be an m x n matrix. Write the matrix [ Qr₁ Qr, ] as…

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Q: Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a…

A: This is an optimization problem l. We will solve this using differentiation.