Find the average height of the paraboloid z = x² + y² over the square 0≤x≤3, 0≤ y ≤3. The average height is (Type an integer or a simplified fraction.)

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Q: Find the mass of the intersection of two rods with constant mass density p that is formed by the…

A: We can solve it as follows

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Q: Find the distance from the point (-4,-6,4) to the line a(t) = ( – 5, 1, − 3)t + (− 7, — 4, 7) FORCYY

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Q: The average monthly rent for a 1000-sq-ft apartment in a major metropolitan area from 1998 through…

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A: Given function k( x ) = 3xx2 + 4

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A: Given that  a spherical planet with a radius of 3 units and let its origin is centered at (0 , 0, 0…

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Q: 1. Determine the area bound by the following functions and double- check your answer.. y = 4x² + 1,…

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Q: 6) Differentiate y=2 cos (z) + 6cos¹ (z).

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Evaluate the definite integral S²₁(9ti +t³j+t¾ k)dt = [[ 0 ]i] ¹₁ + [[ 0 ] i] ¹₁ + [ 0 ]i] ¹₁ = 0

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Q: Find the derivative. f(x) = 8√√2x² +7 f'(x) =

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Q: The sides of a square baseball diamond are 90 feet long. A player is between second and third base,…

A: The sides of a square baseball diamond are 90 feet long. A player is between second and third…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

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Q: Use Lagrange multipliers to find the points on the cone z² x² + y² that are closest to the point…

A: Lagrange multiplier is used to solve many problems related to finding the maximum or minimum value…

Q: reduce the equation to the intercepts form. Draw the line. 5. x + 2y = 9 6. 7x – y = -1

A: solution:-(5)x + 2y = 9the intercepts form of line is given byx + 2y = 9divide both side by 9 we…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: St²y" t²y" — 3ty' + 4y = t² ln t, [y(1)=1, _y′(1)= 1.

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Q: Find dv/dx by implicit differentiation, given that -x^2/v^2-cos(3v)=-8

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Q: Sketch the region of integration and change the order of integration. *9 *√81 - y² 1₁ 0 -9 JO f(x,…

A: The given integral is:∫-99∫081-y2 f(x,y) dx dy

Q: The demand for a new computer game can be modeled by p(x) = 55-4 In x, for 0≤x≤800, where p(x) is…

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Q: Use Cramer's rule to solve the system of equations 2x1 + x2-3x3 21-2x2 + x3 3x1 +4x22x3 = 1 = 0 =…

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Q: Evaluate the integral Note: Use an upper-case "C" for the constant of integration. I 9 | ² ²+16 dz

A: To evaluate the following integral. ∫9x2+16 dx

Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. (If the…

A: To determine whether the series is convergent or divergent.  If it is convergent, then to find its…

Q: Complete the following steps in order to find a vector-valued function r(t) that satisfies the…

A: Please see the below picture for detailed solution.

Q: 3. If F(x, y) = 3x¹y³ – 2x²y³, find F(x, y)/y²

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: ) Derivatives of trigonometric function and inverse trigonometric functions 6) Differentiate y 2 cos…

A: Note:- Since you have posted multiple question in this question which are not interlinked so i have…

Q: Suppose the amount of a drug left in the body t hours after administration is mg. Find the rate of…

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Q: d dx Prove that (csc(x)) = -csc(x) cot(x). d dx (csc(x)) = || = = d dx sin²(x) 1 sin(x) 1 -csc(x)…

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Q: Use cylindrical coordinates. Evaluate x² dv, where E is the solid that lies within the cylinder x2 +…

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Q: For each function, use our techniques to sketch the graph. Include asymptotes, at least one…

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Q: 3. Let f(x,y)=x²y/(x² + y²). (a) Show that f(x,y) goes to zero if (x,y) goes to (0,0) along any…

A: Solution: (a) If (x,y) approaches (0,0) along the straight line y = mx, then we can substitute mx…

Q: Find the gradient of the function at the given point. g(x, y) = 13xe/x, (17, 0) Vg(17, 0) =

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Q: Use l'Hôpital's Rule to evaluate lim t→0 lim t-0 5 sin (416) - 4t = 5 sin (416) - 4t (Type an exact…

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Q: Calculate the double integral of f(x, y) = over the triangle with vertices A=(3,7), B = (8, 12), C =…

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Q: Let f(x) = 2x² + 13x + 15 3x2 + 11x + 6 As →→∞o, y → As a → ∞, y → - As →→-3, y → A Consider the end…

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Q: Evaluate the integral below, where B is the ball with center the origin and radius 2. J√√6 (x² + y²…

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Q: find the revolution of the solid of revolution generated by revolving the region bounded by y=ln(x)…

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Q: Find the volume of the solid whose base is the region in the xy-plane that is bounded by the…

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Q: A roadside wall has a zigzag pattern on it as shown. The two longest lines are each 2 m long, then…

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Q: 10) Consider the following two functions p(t) = and 7e-2)-7 t-2 P: R R if 0 2 q: R→R q(t) =…

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Q: Find m so that x-2 is a factor of 2x³-8x +mx+18.

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Q: A restaurant purchased kitchen equipment on January 1, 2017. On January 1, 2019, the value of the…

A: The given modeled is: Vt=14550 e-0.16t On January 1, 2019, the value of the equipment was $14,550.

Q: Calculate the double integral. Sk [[[x sec²(y) dA, R = {(x, /1105x58,0sys X y) y) | ≤ ≤ ≤ R 2}

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Q: sing the following graph of the function f, aluate the limits (a) through (i). 10 -2 8t 6- -2 -4 y X…

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Q: (x²-5x²+17x³-15x+45)÷(x²-3) =

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Q: (g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6. O 30 20 -10 10 O 30 20…

A: Given that , ft=t3-9t2+24t

Q: Write a polynomial f(x) that satisfies the given conditions. Express the polynomial with the lowest…

A: NOTE: Refresh your page if you can't see any equations. . the given complex zero is x=4-8i so the…

Q: is this fully simlified ?

A: Find the derivative of  f(x)=82x2+7