Find the volumes of the solids generated by revolving the regions bounded by the graphs of the giveN equations y=6-2x- x² and y= x +6 about the x-axis.

Q: 1. In a study of Laguna State Polytechnic University students, 55 had taken Mathematics subject, 105…

A: We need to solve by using Venn diagram. NOTE - As per Bartleby's guidelines we can solve one…

Q: Given f(x) =x2- 1, find the value f(2)

A: Given f(x)=x2-1

Q: Evaluate the summation 5/32 31/32 93/80

A: This question is based on summation.

Q: Use the Table of Laplace Transform to find the Laplace Transform of the given function. a. te-3t +…

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Q: Find the area under the graph of the function over the interval given. 32) y =x2 +1; [0, 1] A) D)를…

A: Given :y=x2+1   0,1

Q: Use Lagrange Multipliers to solve the following: Maximize f(x,y,z) = 4x + 2y + z subject to x^2 + y…

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Q: Q28- The value of e-(In+1 )n is a) (-1)" e--1 b) (-1)"e" c) (-1)" e-+1 d) (-1)" e-"

A: We have to find value of  e-(in+1)π

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

A: In a particular very small region, the consumer price index, C, depends on the current value of…

Q: - 4( Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9 ej- e "k. Compute the derivative of the following…

A: topic - dot product and derivative of a function

Q: Find all critical points of the function f(x) = sin¬'(x) – 8x for –1 < x < 1. (Use symbolic notation…

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Q: Evaluate the integrals in the following questions using integration by parts for In (x + x²) dx

A: Given ∫ln(x+x2) dxTo evaluate the integral using Byparts rule:

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A: Given f(x) =x^3+3x^2+2 Find local extrema

Q: 21) y" – 2y' +10y = 0, y(0) = 3, y'(0) = 3.

A:

Q: What are intervals of concavity of the function f(x) = -2x + 6x² – 3 ? %3D

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Q: To find the distance.across a small lake, a surveyor has taken the measurements shown. Find the…

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Q: Consider the function f(x) = x4 + 2x3. (a) Find the x- and y-intercepts of the graph of f (if any).…

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Q: Why does the graph of x2 + y2=4x has it's center at point (2,0)? and not (0,0). And how to try to…

A: Here equation we have given is of a circle : x2+y2=4x.

Q: What is the absolute minimum value of the function f(x) = x³ – 3x2 on the interval [-1, 4] ? а. 16 O…

A:

Q: In finding the area underneath a curve, which among the Riemann sums and definite integral is the…

A: Riemann Sums : As we know that a Riemann sum is an approximation of a region's area, obtained by…

Q: Find the local extrema of f(x.y) =x²+y³+3xy and determine whether they are local maximum, minimum,…

A: To solve the given extrema problem.

Q: 161 n + e 20 n 2n + tan (103 n). CO The sequence is n=1 O divergent as its limit is o 161 O…

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Q: 2 and v2 = 3 be Work Problem 2 : Let vj = two vectors in R?. (a) i Determine whether v = belongs to…

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Q: Given. f: {a, b, c, d} to itself f(a) = d, f(c) = a, f(a) = b, f(d) = c, f(b) = a Which of the…

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Q: a) Determine whether the series 11n? + 8n + 32 is n³ + 3n² – 7n+ 1 n=1 convergent or divergent. b)…

A: !) The given series is: ∑n=1∞11n2+8n+32n3+3n2-7n+1 Let, an=11n2+8n+32n3+3n2-7n+1; n≥1&amp; bn=1n;…

Q: Q2: Find a root of x – 0.5 – 2-2x = 0 by using Newton-Raphson method correct to 4 decimals so that…

A: We have to find the root of given function by Newton Raphson method.

Q: Consider the following. f(x, y) = xy2 4 r= 4 r= 3 (a) Set up an iterated integral in polar…

A:

Q: y" + 25 y = 10(cos(5t) – 2 sin(5t)), y(0) =1, y'(0) = 2. %3D %3D

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Q: Sketch the graph of a function f with domain [1, 5] satisfying all the following conditions: •…

A: This question can be solved by the concept of nature of graphs.

Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

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Q: Solve triangle ABC if LA = 41.4, a = 186.2, and b 244.4. %3D %3D sin B = %3D

A: answer is in next step

Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

A: Given, Aim: To Find AC

Q: a) Determine whether the series Σ is convergent or Vn3 + 4n + 5 n=1 divergent. b) Determine whether…

A: We have to find if the given series is convergent or divergent.

Q: In the standard (x,y) plane, what i the distance between (3, 4) and ( 2)?

A: Topic:- geometry

Q: Prove that 17 is the only prime number of the form n- 64.|

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Q: 5) Find the area enclosed by the circle r = 3 cos 0 and the cardioid r =1 + cos 0.

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Q: If P(t) is measured in dollars/hour and t is measured in hours, what are the units of P'(t)? O…

A: Given P(t) = dollars/hour P'(t)=d/dt(dollars/hour)  We are derivating with respect to time

Q: 0 cos n0 do

A:

Q: Problem #7: A rectangular garden is fenced on three sides, and the house forms the fourth side of…

A: Given problem:- A rectangular garden is fenced on three sides, and the house forms the fourth side…

Q: Find the following for the vectors u = 6i – 5j + 7k and v = - 6i + 5j - 7 k. a. v•u, v|, and u b.…

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Q: so Je cos T0 d0

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Q: Identify the polar coordinates of the point with the given rectangular coordinates. (-6, - 6/3) 7T…

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Q: Part (3) Double Integration in Cartesian coordinates: 1) Find the volume of the solid under the…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Solve the system of equations. If the system has no solution, say that it is inconsistent. X + y - z…

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Q: Let U be the universal set of natural numbers less than 11. Consider the following two sets. A = {9,…

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Q: Find out all the relative minimum and maximum values, and sadle points of the function h defined by…

A: Here we have h(x,y)=x3-3x+3xy2 .............................................. (1)

Q: 8. dx x² + 36 0.

A: The given integral,        ∫08x3x2+36dx

Q: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

Q: Solve the system of linear equations бу + 4z %3D -24 Зx + Зу -6 %D 2x 3z = 4 (х, у, 2) %3D (||

A: Here we have to solve the system of linear equations. 6y+4z=-24 ..................... (1)3x+3y=-6…

Q: Calculate the left rectangle approximation of 3x- dx using five subintervals.

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Q: Using integration, derive the Laplace transform of: * L(sinh at)

A: This is a problem related to integration. based on the general formula and concept we will answer…