A piece of cardboard measuring 14 inches by 12 inches is formed into a an open-top box by cuttin squares with side length x from each corner and folding up the sides. Find the value for x that will maximize the volume of the box . show picture

Q: Work Problem: Let f be a function defined by - f(x,y) = 6x³y4 – 7y. Evaluate the following: Vƒ(1,…

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Q: Evaluate the two integrals given the graph. The two parts of the graph are semicircles. 1. 4 f(x) dx…

A: Given both the circles are the semicircles a) ∫14f(x)dx =area between x = 1 to x = 4

Q: Let z(x, y) Calculate дz მs дz - = = дz მ - 7x² - 9y2 where x - & дz St by first finding 8s + 5t & y…

A: To solve the following problem by finding the partial derivatives

Q: 4x² - y² 5 (-1, -3) that has a positive a component. For the function f(x, y) = 3 find a unit…

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Q: What is the differential equation of the given 2 parameter family of solutions? 6 y = c₁e sin x +…

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Q: Evaluate the summation: η Σ η3 – 1 nEZ\{1}

A: The summation to be evaluated is  ∑n∈ℤ\ 1∞nn3-1.

Q: have a horizontal tangent? X = help (numbers) f(x) = 10x² + 15x² 60x 60

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Q: Would it be DNE ?

A: Let's solve. In above answer calculation mistake is there.

Q: What is the inverse of the function f (x) = 3(x + 2)² – 5, such that x = -2? Of(x)=-2+, +5…

A: Given query is to find the inverse of the function.

Q: Let z(x, y) Calculate дz მs дz 2t = дz მs & 7х2 + y² where x = s + 8t & y = дz St by first finding…

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Q: • f (8. +12) de dx + • / ( 1 + ₁² + 0² - 2²/1) dx [sin(3x)dx

A: (1).The given integral is:∫8-x5+4x dx

Q: Let f(x) = 2 sin(x). a.) |f'(x)| ≤| b.) By the Mean Value Theorem, f(a) − f(b)| ≤ la - bl for all a…

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Q: 1- Estimate using linear Approximation. 3 192 - 1/10 19

A: Let's estimate value by using linear approximation.

Q: Given f(x)= X-4 O[4, 12) U (12,0⁰) 0 [--4, ∞) and g(x)=√√x+4, what is the domain of f(g(x))? O(-∞,…

A: Givenf(x)=1x-4 and g(x)=x+4We need to find the domain of f[g(x)]

Q: The Venn diagram shows sets A, B, C, and the universal set U. Shade (A'U B) n C' on the Venn…

A: Venn diagram is used to represent  Let's first draw the Venn diagram step by step.

Q: Use the figure to evaluate the definite integrals S 2 1 y -1 -2. 1 2 y = g (t) 3 4 +t 5 g(t) dt and…

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Q: A local club is arranging a charter flight to Hawaii. The cost of the trip is $577 each for 81…

A: Given query is to find the maximum revenue.

Q: Transform the following differential equations to the standard form (dy/dx) + A(x)y = B(x) OR…

A: We can solve the given differential equation by using the integrating factor method.

Q: Concept check: Evaluate the following integrals: 1.₂ dx 2³√x + √x

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Q: 1 3. Convert the integral IM x² + y² + z² and evaluate it. (Think about why converting to spherical…

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Q: c Instructions for the following questions write your answers and working out on paper. For a full…

A: Let's find revenue function, profit function and price at 3 units.

Q: 1) An antiderivative of a function f (x) is a function F (x) such that F ′(x) = f (x). Find any…

A: Note:-     Given functions:- a) fx=12x2+8sec2x b)gx=x+6sin2x

Q: One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 9 hours. How…

A: Solve the given

Q: Second Derivative Test 1. Find the first derivative of the function g(x) = 6a³ + 45x² + 108. g'(x) =…

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Q: Find df (5x + 2y)dA where R is the parallelogram with vertices (0,0), (-4,4), (3,2), and (-1,6). R…

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Q: Let 5x³ - y³ + 52³ - 4xyz - 874 = 0. дz Use partial derivatives to calculate and ?х дz ?х дz ду…

A: To find the partial derivatives at a given point.

Q: Textbook -5-4-3 a < X < 56 4 3 2 mpy 2 -3 -4 Videos 2 3 The function graphed above is decreasing on…

A: The Solution is given below

Q: Question 6 A spherical snowball is melting in such a way that its radius is decreasing at a rate of…

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Q: Find the equation of the line tangent to the graph of f(x)=(ln x)5 at x=2. Answer in slope…

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Q: 53. sec² x 1 + sin x sec² x - sec x tan x cos² x

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Q: Find the area of the shaded region. r = 5 + cos(0) -6 -4 -2 y 4 2 -2 -4 LC 2 4 X

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Q: Find d2w/dz2 for the given function.   w= 8z2e2

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Q: Find the first derivative f' and the original function f. /' ( - ) = ¹¹ / ( - ) = ( 11, f"(x) =…

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Q: Which of the following expresses 1-4+16-64 +256 in sigma notation? 5 a. Σ(-4)k-1 k=1 4 b. Σ (-1)…

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Q: 1. f'(x) and ƒ' (7). Show all work, no decimals allowed in your final answer y -Cos (x) Tan(x)…

A: Given query is to find indicated derivative.

Q: cab ride costs $1.70 plus $0.10 per tenth of a mile traveled if you use the Green Cab Company. The…

A: Given query is to find the distance when both company cost same.

Q: Find the value of each expression without using a calculator. 1.) a. sin 180° b. cos 180° 2.) a.…

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Q: Evaluate the following sums. 9 (2) Σ 3 k=1 500 (b) Σ 9 k = 1 264 (c) Σ k = 2 20

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Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

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Q: Given an interest rate of 5.5% compounded daily (ie: compounded on each calendar day), determine the…

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Q: write the cubic polynomial function f(x) in expanded form with zeros -4, -3, and 2 given that f(1)=…

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Q: (x+10)² 144 2. Express the equation draw its graph. in its general form, find its elements and…

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Q: TION -2x-8 b) ²+4 <- 6x +5 INVESTIGATING THE GRAPHS OF QUAC LINE OF SYMMETRY OPENS UP OR DOWN?…

A: We have to find the following conditions according to the given information

Q: 3. Find the volume of the portion of the ball x² + y² + z² ≤ 1 lying above the plane z = 3/5. (I…

A: Given that  solid is bounded by   x2+y2+z2≤   and lying above the plane z=35

Q: Find the centroid of the lamina bounded by the x- and y-axes, the line x = 2, and the graph of y=e*.…

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Q: 3. The derivative of a function is given by f'(x) = -63x² - 12x + 18. Give 3 different functions…

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Q: K Consider the function f(x) = - (a) lim f(x) = X→∞0 3 4x³ + 18x² + 18x lim f(x) = (a) Evaluate lim…

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Q: If the following series converges, compute its sum. Otherwise, enter oo if it diverges to infinity,…

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Q: Set up a triple integral in cylindrical coordinates for the volume of the solid region E, where E is…

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Q: 8. 00 ro a. b. C. d. a 18€²-90€ +72=0 t²-5t + 4 = 0 18€²-4+ ++4=( e. Let s(t) = 6t³ - 45t² + 72t be…

A: (8) The position of particle is given as , st=6t3-45t2+72t