A rectangular metal tank with an open top is to hold 864 cubic feet of liquid. What are the dimensions of the tank that require the least material to build? The tank that requires the least amount of material to build has length ft, width ft, and height (Simplifu

Q: Find the indefinite integral. √4x In (7x) dx √4x In (7x) dx =

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Q: 2 show that V(x, y) = x 'f (2x+y) is the general Solution of : Xav dx 2x du ду = V

A: We can show given function is a solution of the given equation .

Q: 1) Approximate (3+x-x²) dx with a left-endpoint Riemann sum using four equal subintervals. 2)…

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Q: 6x² + 5x + 16 S x3 + 3x² + 2x + 6 5 Injx+31+ In (x² + 2)√2 tan ¹() + C Option 1 5 Injx +31+ In (x² +…

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Q: i) n=1 1 1+2+3++n j) 1 n In n(ln(Inn)+1) k) 2" +n n!+1 n=1

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Q: ✓ Solve the following linear programming problem using the graphical method Min (Z)= 20X+30Y…

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Q: Let F be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny). Let C be the unit…

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Q: Solve simultaneously x (t) + x' (t) − y (t) + z' (t) = 4 y' (t) + z(t) = 0 2x(t)+y(t)+z(t)=0 where x…

A: Given the system of differential equations x(t)+x'(t)-y(t)+z'(t) = 4  ......(1) y'(t)+z(t) = 0…

Q: Solve it neatly, correctly, and comprehensively.  2. An open box is made from a thin sheet of…

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Q: find the volume of a solid limited by a cylinder = x^2+y~2=25, by a plane = x+y+z=8

A: Concept: Volume using triple integrals: Let D be a space region that is closed and bounded. Let a…

Q: Find the eigenvalues of A³ for Enter the eigenvalues in increasing order. Eigenvalues of A³ are: i i…

A: Cayley Hamilton theorem and basic property of eigenvalues are used

Q: 3. Output, P, is produced using two inputs, K and L, according to P= f(K, L) = 2 + KL-2 5 1) Find…

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Q: Solve Zxy and Zyx when Z=2xy³ - 3x²y²

A: To find the partial derivative

Q: अ 250 -x5/2 - 2x³/2 + +बेकर 9 x³ - 2x² + x − 1 -

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Consider the following vector fields: F = (3x²e²ª, 2x³e²y + 2 cos y sin y) and Ġ = (y+z, x+y, z —…

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Q: 4x Compute the values of dy and Ay for the function y = e + 3x given x = 0 and Ax = dx = 0.02. Round…

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Q: a) Sdx 5

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: In spherical coordinates, the equation below describes what? O a plane O a cone O a sphere O a…

A: topic- spherical coordinate system

Q: F=x²y³z¹i-xyzj+(x+y+z)k

A: The vector field is F→=x2y3z4i^-xyzj^+(x+y+z)k^

Q: Q.2// Find (A) f sin¹ (x) cos5(x) dx (B) f 4t³-t²+16 t t² +4 dt (C) Use improper integral to find ²…

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Q: - show that V(x,y) = x 'f (2x+y)

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Q: Determine the magnitude of the vector difference V' = V₂ - V₁ and the angle 0x which V' makes with…

A: We have to find the vector and angle.

Q: Evaluate S√9-4x² dx a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

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Q: o classify the following PDES :- 227 ахг <-2 822 буду +2 82 дуг =x+3y 2 X •x2 Ихх - 2 xу Иху +ў Иуу…

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Q: X p(x, y, z)=xz²+sin (y) ex

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Q: solve by differential √226

A: Let's find value by using differential.

Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: The line passing through the points 1,3,0 and 2,4,4

Q: 7) Suppose the population of Detroit was 1.5 million in 1990 and 1.0 million in 2002. If the city is…

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Q: 2x² + x + 3 x³ + x dx In[x] + In (x² + 1) + tan^³(x) + C Option 1 3 In]x] +In (x² + 1) + tan¹(x) + C…

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Q: A sales analyst determines that the revenue from sales of fruit smoothies is given by - 70x² + 420x…

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Q: If u and are non-zero vectors and Proj=0, then which one of the following must be true? O The two…

A: Two vectors u and v are orthogonal if u.v =0 .

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

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Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

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Q: Find the characteristic equation, the eigenvalues,

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Q: The area common to the circle > = 3 and the cardioid r = 3(1 - cos 9).

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Q: Draw a direction field for the given differential equation. Based on the direction field, determine…

A: We have to draw the direction field for the given differential equation.

Q: Find the area inside one leaf of the rose: r = 5 sin(40)

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Q: Consider the following. '6 dt Jo 36 + t² Let t = 6 tan(0) and determine the following.

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Q: Find the general Solution of the complement of the following differential equation y"- 3y"+9y'+ 13…

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Q: Find the general Solution of the complement of the following differential equation y"-y" - y'- 2y =…

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Q: convert the Following differential equation into a perfect equation and then Find its general…

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Q: Find the general Solution of the following PDES Du -5X -3x = 2 +4, исx; c) = 32 + 2e du ду 3e Dx…

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Q: Integrate. √7x²√x+2dx= (Use integers or fractions for any numbers in the expression.) √x+2 dx

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Q: (b) the volume of the solid B that lies above the cone z = 3r² + 3y² and below the sphere x² + y² +…

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Q: Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx − (2xy + x²) dy…

A: A detailed solution is given below.

Q: Let f(x) = 3 cos 2x + sin² x. a) b) Show that f'(x) = -5 sin 2x. Зл In the interval <x< one normal…

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Q: Find all the critical points of the following functions and classify them as local maximum, local…

A: First we need to find the critical point and then we should apply the conditions to approach it as a…

Q: Prove each of the following. (a) Given a real number a > 1 with a N, show that there is some natural…

A: a) As a is a real number, then it can be written as sum of a natural number and a fraction.  Hence,…

Q: =: Triangle may not be drawn to scale. pose a = 3 and b = 8. an exact value or give at least two…

A: Please refer to the image below

Q: dx | | dt dy dt dz dt = 3x + 2y + 4z = 2x + 2z = 4x + 2y + 3z

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