³ [] (2² + y²) p(x, y, z)dV where p is the density function. Moment of inertia about z is calculated as Let E be the solid below z = 32 - x² - y² and above the square [- 4, 4] × [ − 4, 4] Given the solid has a constant density of 5, find the moment of inertia of E about the z-axis.

Q: determine whether the given series converge or diverge. 20. (-0.99) ¹+1 n=5

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Q: In geometric sequence the common ratio is denoted by RO

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Q: equilibrium point, and (c) the producer surplus at the equilibrium point. 7 1 -x+ 27, S(x) = x+3 10…

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Q: Can you solve this? 10x8 5x4 A) 2x² B) 2x¹2 = ? C) 2x4 D) 2x32

A: Solve the given

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A: Solution

Q: The vectors u = (5, -4,0) and v = (-4,-5, 4) are orthogonal. Select one: O True O False

A:

Q: Let f(x) = be a piecewise function. Evaluate So fo f(x)dx= 3x²+2, 2x - 3, if x < 2 if x ≥ 2

A:

Q: z=(4xy)/[(x^2)+(y^2)] (a) (partialz)/(partialx)

A: We have to find the partial derivative.

Q: Use logarithmic function to find dy/dx, if y=(x^2+5)^sin (2x)

A:

Q: etermine the net area.

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find all values of x in the interval [0, 2(pi)] that satisfy the equation.  14 + 7 cos(2x) = 21…

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Q: Find the derivative of the function. f(x) = ex In(x³) f'(x) = X

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Q: Solve DU 11 dx 4x+3 x³ +2x² + x

A: ∫4x+3x3+2x2+xdx=∫3x-3x+1+1x+12dx=∫3xdx-∫3x+1dx+∫1x+12dx=3lnx-3lnx+1-1x+1Add a constant to the…

Q: Find the volume of the parallelepiped determined by the vectors a (3, 4, 1), b = (0, 2, 4), = (2, 4,…

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Q: Find the general solution of the differential equation. dy dt 8 ,t20 The general solution is y=.

A:

Q: Using triple integrals, calculate the volume of the set in 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤z<5-x²-y² Ps:…

A: Find Volume of the set in 0&lt;=x&lt;=1, 0&lt;=y&lt;=1,&lt;=0z&lt;=5-x2-y2 .

Q: Write an equation for the transformed logarithm shown below, that passes through (2,0) and (1,3) N 4…

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Q: Evaluate the following integral. Sx12xdx x12*dx = (Type an exact answer. Use parentheses to clearly…

A:

Q: A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: A tank contains 240 litres of fluid in which 50 grams of salt is dissolved.pure water is pumped into…

Q: Your college newspaper, The Collegiate Times, has fixed production costs of $7000 per edition, and…

A:

Q: True or False: We have Select one: O True O False 2 2 2 [ ² x³²dx < [ ²³ x³²dx 1

A:

Q: OLA: Solve the following system by (method of inverse) 2x₁ + 3x₂ = 5 x₁2x₂ = -1

A: Given problem:- Solve the following system by (method of inverse) 2x1 + 3x2 = 5 x1 - 2x2 = - 1

Q: The equations of three lines are given below. Line 1: Sy=-3x+4 3 Line 2: y=-=x-5 5 Line 3: 10x+6y=6…

A:

Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: Juan Dela Cruz wants to deposit ₱5,000 every quarter at 16% compounded quarterly for 5 years. How…

A: We have to find out solution

Q: The value of the definite integral is Select one: O 16 3x²dx 0-8 O none of the others 08 0 0

A:

Q: Find a rule for the derivative of the product of four functions f,g,h, and k. Use your result from…

A:

Q: Evaluate the infinite series by identifying it as the value of a derivative of a geometric series.…

A: Solution

Q: ate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: Q2: Fill in the blanks : 1- ff f(x,y)dydx represents the. 2- y" +(3y')5 - sinx = 4 of order 3-ye…

A: Since multiple questions are asked I am answering first 3 subparts

Q: Let R be the region bounded by y=x, x= 1, and y = 0. Use the shell method to find the volume of the…

A:

Q: Using Rolle's theorem for the following function, find all values c in the given interval where…

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Q: Let a = 5j + k and b - 27 + 3 + 2k. Find - 3ā – 36.

A: We can find the given vectors.

Q: Give a possible formula for the function below. Let A = (1, 21) and B = (2, 147). Use the general…

A: Given problem:- Give a possible formula for the function below. Let A = (1, 21) and B = (2, 147).…

Q: Put the following program in standard matrix form: Z = X₁ + X₂ X1+ 5x2 <5 2x₁ + x₂ ≤ 4 maximize:…

A: see below the answer and the explanation

Q: = Consider the region B under the graph of y x = [5,7], and above the x-axis. 2² +7 x+5 J Estimate…

A: We want to find estimated area using left and right endpoints.

Q: * he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

A:

Q: 1₁ f(x)dx = 6 ln([x]) - 6 ln(|x]) — -—-cos(5x). -cos(5x) - 3e + x² + 6x + C

A:

Q: The intervals on which f(x) = x² ln x is increasing and decreasing, and the intervals of concavity…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 42. y=+on [1/2,2] 6

A:

Q: Let à = and b= . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

A:

Q: e intervals on which f(x) = x² In x is increasing and decreasing, and the ervals of concavity and…

A: Topic:- application of derivatives Definition :-  Inflection point :-  The point of inflection or…

Q: Find dy/dx, given that xy^3 -3y^2 +xy=1-3x

A: We have given a function y in term of x, and finding the derivative of that

Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

A:

Q: Find the sum of the series: n=0 (-1) 16-2 (2n)!

A: Find the sum of the series (-1)n16n-2/(2n)! from n=0 to infinity.

Q: Use R6 to determine the area under the curve for f(x) = (2-1) on [2,5].

A: Given that fx=1xx-1 To find : Area under curve of fx on 2,5Solution :

Q: Perform the row operation 3R2 + R₁R₁ on the matrix below. 3 2 4-6-8 1 1-3 2 (X3 (888) 4-6-8 3R2 + R₁…

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Q: 3. (a) Solve the differential equation (x+1) ª¹ = y +e³(x+1)² . dx (b) Form the differential…

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Q: Find the constant of variation when one exists and write it in simplest form. Direct variation…

A: We have to find out solutions

Q: DE 1. xy(5) y(4) + x²y"" = 2yy' TYPE ORDER DEGREE LINEARITY

A: