an open box is to be made from a 2 foot by 3 foot rectangular piece of metal by cutting equal squares from the corners and turning up the sides. Find the volume of the largest box that can be made in this manner. Round your final answer to the nearest hundredth.

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A: Here, the given vectors are P(-3,1,5), A(1,1,0) & B(-2,3,-4)

Q: x³3-* dx -x³3-*In (3) + 3x² 3¬× ln²(3) – 6x 3¬×ln³ (3) + 6 3¬× In*(3) + C A B -x³3¯* ln(3) + 3x² 3¯*…

A: Let's find.

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A: Using bernoulli's differential equations, solve this differential equations.

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Q: ((- +3) dt 21.

A: the given integration,       ∫0245t3-34t2+25t dt

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A: Given that,     f'(x)=x+510-x15-x

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Q: 3. 8х' + 13 2. S 3 4x' + 8х + х + 2 2

A: integration

Q: 【コxマー52

A: Given problem:- ∫x2x2-53dx

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Q: Which of the following gives the formula for the inverse of the function x + 3 f : R \ {-7/2} → R \…

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

Q: Determine whether the improper integral 3-2x) /2 dr onvergent or divergent.

A: We have to find the integral

Q: y = Vx +1(3– x)* (x- 3)(5x + 1) 2/x +1 b Find the x-coordinates of all points on the graph of y…

A: To find the derivative of given function.

Q: Derive the Taylor series about -1 of f(x) Determine its interval x2 | of convergence.

A: Here we have to find taylor series and then interval of convergence .

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Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

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Q: Find the area of the triangle with vertices P(1,5, –2), Q(0, 0,0) and R(3, 5, 1). NOTE: Enter the…

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Q: 5) x²dx + y(x – 1)dy = 0 %3D

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Q: A wire of length L- 100cm is divided into two parts. One forms a circle and the other forms a…

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Q: Find the vector component of v = 2i – j + 3k along b = 2i + 3j + 6k and the vector component of V…

A: Given : v=2i-j+3kb=2i+3j+6k   To Find : a) vector component of v along bb)vector component of v…

Q: Determine the integrals of the following functions. Express the final answers in simplest form. 8 5…

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Q: Q1) Find 2/3 dx a) Jas x*/9x² – 1 V2/3

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: D = {(r, y) : 1 <Ise, 0<yS In(r)}

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Q: Find the gradient of the function at the given point. g(x, y) = 4xey/x, (11, 0) Vg(11, 0)

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Q: Integrate the ff.

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-8, 0,…

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Q: Find the derivative. y = e2= . 8x3 24x?e2 + 16x4e2« – 1 O 2e2a . 24x? 24x e2 + 16x³e2* O 2xe2a…

A: We will find the derivative using Chain rule.

Q: (-1,3) -2,1) (0,1)

A: Topic = Functions

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A: Given problem:- ∫∫D x3 dA        D={(x, y) : 1≤ x≤ e, 0≤ y≤ ln(x) }

Q: Suppose that the bacteria in a colony grow unchecked according to the Law of Exponential Change. The…

A: Given:    Since we have given that Number of bacteria initially = 1   It triples in number every 30…

Q: 8) Find a power series representation and determine the interval of convergence for 2 f(x) = 3 – x

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Q: |lv|| = 4, e = 3.8° V = Need Help? Read It

A: We will find the component form of v.

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A: answer is in next step

Q: answers in terms of i,j and k.

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1) Vw(19, 5, -1) =

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Q: Find the (natural) domain of the function x + 1 2х — 1 f (x) = Select one: a. (-0, –1] U (1/2, ∞) b.…

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Q: please answer 9 and 10 only Find the general solution of each differential equation, and when…

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Q: The sum of two positive numbers is 16. Find two numbers such that the sum of the squares is a…

A: Given problem:- The sum of two positive numbers is 16. Find two numbers such that the sum of the…

Q: Find the vector component of v = 2i – j+ 3k along b = i+ 2j + 2k and the vector component of v…

A: We have to find the vector component along another vector