A box with no top and a square base has to be designed so that its volume must 108 cm³. Find the dimensions of the box if the surface area is a minimum.

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A: Given: Let R be the region bounded by y=4-x-22 and y=x. To Find: 4 To write an integral expression…

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A: Given, f(x)=x3-sin(x)

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A: Given problem:- Consider the logistic equation in the form P'(t) = CP − P2. Solve the logistic…

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A: Here, to find the equation of the plane that passes through the point P14,-12,7 and contains the…

Q: 56. Solve the integral of (x + 2y)dxdy with respect to x from x=y and x = y^2 and with respect to y…

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Q: 3x2+2 0 2x²+4x+3 So dx

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Q: A region bounded by fly) = y + 1, y = 4, and x = 1 is shown below. Find the volume of the solid…

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Q: -4 Challenge #1 y = 2x 0 Adjust the equation so the exponential function passes through the points.

A: topic- exponential function

Q: ) .  Consider a minimal threshold value for a species to survive, T. One way to add in this factor…

A: answer is in next step.

Q: Find the curl of the vector field F. F(x, Y, 2) = arcsin yi+ V1 - xzj + yêu y²k

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Q: Problem 16. (a) Calculate the following antiderivatives: //=/ dx = (b) / -55 (c) / 2e" dx = [ -5 sin…

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A: Here we have to find the sum.

Q: 3. Find the general solution of the differential equation y(4) — 4y" = t² +et.

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A: We have to find the equation of the relation whose vertex is lower than the origin and left to the y…

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A: y if the equation defines y as a function of z but not vice versa, x if the equation defines z as a…

Q: The velocity of an airplane flying into a headwind is given by v(t) = 30 (25-t²) mi/hr for Osts3 hr.…

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Q: Find the curl of the vector field F. F(x, y, z) = (2y - z)i + e²j + xyzk

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Q: Suppose dP dt and P(1) = 4. Answer the following. 3) Separate the differential equation, then…

A: The objective of the question is evaluate the indefinite integral.

Q: 1- Find the inverse of Laplace transform of log s²+1 (s-1)²,

A: To find inverse Laplace transform:

Q: ---2 y=g(x) y=f(x) The graph of f is shown in red, and the graph of g is shown in blue. Use the…

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Q: Problem 12. Find the absolute maximum and absolute minimum values of the function over each of the…

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Q: Which of the following series should be used to determine the divergence of the series Σ, V5n2+2n+4…

A: Given :- ∑n=1∞5n2+2n+4n

Q: Evaluate the following limit using L'Hospital's rule. lim (e5z - 2.x) (+) I+0+

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Q: DETAILS ▪. [1.05/2 Points] PREVIOUS AN Cost of Producing Calculators A subsidiary of Elektra…

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Q: 4. Use the Fundamental Theorem of Calculus to evaluate [(-3) -

A: The objective is to find the integral using fundamental theorm.

Q: Using De Moivre's formula demonstrate that sin(3x) = 3sinx − 4sin3x

A: Given that sin3x=3sinx-4sin^3x De moivres formula is (cos x+ i * sin x) ^ n = cos n*x+ i * sin n*x -…

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Q: question 8 please

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Q: Answer the following completely. Given: tan a = 2√√6, a € [0,π]

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Given that , Point =14,-12 ,7 and line x2=y-4-1=z Find the equation of the plane.

Q: 2x + 5 Consider the function f(x) 52+1 For this function there are two important intervals: (-∞, A)…

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

A: Given that the first equation is          x3=y-2-1=z+11  Its parametric form are:    x=3t , y=-t+2 ,…

Q: 2 y = In (x-√x²-1), for 1 ≤ x ≤ √/485 (Hint: The length of the curve is (Simplify your answer)

A: Topic:- application of derivatives and integration

Q: Verify the Divergence Theorem by evaluating F.NO N ds as a surface integral and as a triple…

A: To verify the divergence theorem. And to evaluate the surface integral.

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A: Here we have to find the value of trignometric functions.

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Q: 17 prove 4 Cos" ☺ - Sin" 0 = Cos20

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Q: At any time t, the rate of growth of the population / of deer in a state park is proportional to the…

A: Solution of given question is written in below steps.

Q: Find the maximum and minimum values of the function g(0) = 30 – 7 sin(0) on the interval ㅠ [0, 1]. 2…

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

Q: (a) AB X AC (b) the volume of the parallelepiped determined by AB, AC and AD

A: As we know the expression for the volume of the parallelepiped is: Vp=AD→·AB→×AC→   The given…

Q: 4 F(s) = 3s7 (s²+3)

A: First to find the partial fraction decomposition of the function: F(s)=43s7(s2+3) For that let,…