A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the origin and the opposite top corner in the first octant on the plane 6x+6y+z=1. What is the maximum volume of such a box?

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Q: Q5. Evaluate the triple integral cos(y²) dz dx dy.

A: The given triple integral is;  Cos(y2), z from 1 to 3, x from 0 to y, y from 0 to sqrt(pi/2).

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Q: L3Q6. If f(x) = 2x – 1 and g(x) = log x, compute (f – g) (x). A.2x – 1 + log x B.2x – 1 – log x

A: Given; f(x) = 2x – 1 and g(x) = log x

Q: question, show all steps so I can understand the problem Use the following property of the definite…

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A: Given z=f(x+at)+g(x−at)To prove ∂2z∂t2=a2∂2z∂x2

Q: From this graph, Find the volume around the X-axis (Use π = 3.14). y = x (0, 0) (1, 1) y=x² R

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Q: dx x√√81-x1 (Type an exact answer.) 16 =

A: Given: I=∫dxx81-x16   ....1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: After his receiving his first income, Juan dela Cruz invested P20,000 in a bank for his future…

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Q: II) Let f be the piecewise function f(x) = x³ + 6x² + 8x x+2 1-x-2, -, x≤-1, x -2 -1 1 1) Sketch the…

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Q: If a = (4, 0, 4), b = (3, 4,-4), and c = (0, 4, 5), show that a x (b x c) = (a x b) x c. 60i + 96j -…

A: Solution: Step-1                         Given if a = 4, 0, 4 ,b = 3, 4, -4, and c = 0, 4, 5, show…

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A: Given :r=5ar=7bsecθ0<5a<7b

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A: We know that for a right triangle , Let hypotenuse is c and other two sides are a and b. Then…

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Q: Exercise 4.4.5 A thin plate lies in the region between y=x and the x-axis between x = 1 and x=2.…

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Q: 5. Determine the area below f (x) = 10 - 2x² and above the line y = 3. 11. 6. Determine the area…

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Q: Q2. If F = (x² − y² + 2xz)ī − (2xz − xy + yz)j + (z² + x²)k, find the of curl F and curl of curl F…

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Q: Calculus Question

A: Disclaimer: Since you have asked multiple question,we will solve first for you.If you want any…

Q: Question 1 [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) = xy…

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Q: the magnitude of the equilibrant? pounds to the nearest tenth.) Media - Copyright © 2022 Pearson…

A: Topic:- trigonometry ratios application

Q: Let r(t) = 21²i+tj+t²k. (a) Find the unit tangent vector T(t) and T(3). (b) Find the principal unit…

A: As per our guidelines we are supposed to answer only first 3 sub-parts. kindly repost others.…

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Q: Calculate f((5x + 2y)i + (4x + 7y) 3) · dr where C' is the circular path with center (a, b) and…

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Q: Convert the point (x,y,z)=(-1,-4,0) to cylindrical coordinates. Give answers as positive values,…

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Q: 1. Which of the following is the general solution of the differential equation Oy²=x² +C að

A: We will solve the differential equation.

Q: rticle subject to a force F(x, y) = (-6y, 6x) moves clockwise along the arc of a circle of radius 4…

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Q: 1. Use the Ratio Test to determine whether the following series converge. Make sure to explain why.…

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Q: (a) By inspection, find a particular solution of y" + 2y = 6. √p(x) = X (b) By inspection, find a…

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Q: The limit is equal to 1312 Select one: O True O False lim n→∞ 3n 2n³ + 1

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Q: 30. Paolo's wife Cristina is not happy about the play area he proposes to build for their children.…

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Q: The average value of the function f(x) =2x + 6 on the interval [2, 5] is Select one: O True O False…

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Q: Find the average rate of change of the function on the interval specified. g(x) = 6x3 − 7  on  [−3,…

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Q: it is the empirical formula for C10H20O5 O C₂H5O

A: Empirical formula  An empirical formula is the simplest whole number ratio of elements in a…

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Q: Evaluate f x²-x-5 x(x²-x-2) dx

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Q: bn = n' ебп

A: Here, the given sequence is bn where bn=nne6n

Q: What is the integral that represents the length of the curve from x 2 to x = 4. Select one: 4 O…

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Q: Given f(x)=2+3x²-x² i. Find the coordinates of all local extrema. ii. iii. Identify the extrema…

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Q: 7x³ - 7x lim x-1 2x² + 2x

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Q: 7. Let C be the portion of the circle x² + y² counterclockwise. (a) (b) Evaluate La xy dy. = 4 from…

A: Let's solve given integral.

Q: 5. Find the divergence and curl of the vector field F(x, y, z) = (xy - 2², 2x+cos(yz), 2y² - sinz)…

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Q: Determine whether the series 2-√√n +∞o Σ √√n n=1 converges or diverges using the Integral Test.

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Q: 1) For each of the following tests, give an example and explanation of a specific series formula…

A: We have to explain the series and give an example.

Q: Use an appropriate Taylor series to find the first four nonzero terms of an infinite series that is…

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Q: Let F = (7yz)i + (2xz)j + (1xy)k. Compute the following: A. div(F) = B. curl(F) =i+j+k C.…

A: We know the expression for the divergence of vector point function F→=F1i+F2j+F3k is:…

Q: Sketch the graph of the quadratic function. f(x) = 3x² + 2 No Solution → Help vertex -10 - -8-7-6-5…

A: We need to draw graph.