The base of a prism is a hexagon inscribed in a circle. If the difference in the circumference of the circle and the perimeter of the hexagon is 4 cm, find the volume of the prism if it has an altitude of 20 cm.

Q: 6-X Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Write the complex number in standard form. V-54

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Q: Question 4 Given y=[ 2 +(x²+1)ª ]³; Find y' O Y = 64 (x2+1)° O (E) None of the choices O y=24x…

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Q: Find the area of the region enclosed by one loop of the curve r = sin(60) 36

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

Q: Find f. f"(x) = 48x2 + 2x + 6, f(1) = 5, f'(1) = -4 %3D %3D f(x) = %3D

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Q: (-1)"(x+3)" n³ + 1 n=1

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Q: Use long division to divide. (Simplify your answer completely.) (9x – 4) ÷ (3x + 2) 2 3

A: Here we will use long division method,

Q: Determine whether the following matrix is invertible by finding its determinant. 4 -14 -56

A: Consider the matrix 14-14-56

Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: dy 8. 6. Which of the following is a particular solution to the differential equation dx when x = e5…

A: Option D is correct answer.

Q: Find the power Series representation for the furiction and determine the radius of convergence.

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Q: Solve the initial value problem. dy 2xy = 8x, у(0) — 0 dx y =

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Q: Calculus III is A. Multi-operational Calculus O B. Momentum Calculus O C. Multi-dimensional Calculus…

A: The course included parametric equation,polar coordinates, vectors ,sequences, Taylor expansion, and…

Q: IV. In each of the following, evaluate | F(1) dt: 4 1. T (t) = - e-2 j– te' k ; a = 0 and b = 2 1+t…

A: To evaluate  ∫abr→(t) dt for given r→(t).

Q: 3. Find Power Series Representation of f (x) around c=0. %3| a) f(x)= and 1-x b) f(x)= (1–x)

A: Solving

Q: Set A 1. Prove using vectors that the points (4, 3, 0), (2, 0, 1), (4, 1, -1), and (2, 2, 2) are the…

A: This is a problem related to vector calculation. Based on the general formula and concept we will…

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A: Use derivative and critical point for finding the absolute maxima .

Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: Solve the initial value problem dy 9(t + 1) – 6y = 18t, dt for t > -1 with y(0) 11. y =

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Q: Use the limit laws to evaluate the limit. (x-19)2 lim X-19 x-361

A: limx→ 19x-192x2-361

Q: For the given matrices A and B find each of the following. (a) A+ B, (b) B+ A, (c) A-B 4. 4 - 1 10 7…

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Q: : Find the volume of the solid obtained by rotating the region bounded by the curve y= -x²+ 10 and y…

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Q: Determine whether or not the improper integral is convergent, and find its exact value if it is…

A: The given integral,      ∫012x+5x57dx Note:     Multiple questions are given, we are answer with…

Q: Find the slopes of the curve y = y - x at the two points The slope of the curve y" = y -x at the…

A: topic - slope of a function

Q: Find the limit. Enter the exact answer. lim sec 3x cos 7x = x

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

Q: 10. What should be the value of A so that S A• sin (6x²) dx = - cos(6x²) + C, ? A. x В. 2х С. Зх D.…

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Q: Find the cylindrical equation for the ellipsoid 4x2 + 4y² + 2² = 1.

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Q: a, Find the points of intersection of the curves y= x² +6 and y= 5x. %3D X, = and x2= %3D b, Find…

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Q: H.W: find the local maxima, local minima, and saddle point of the functions: 4. f(x, y) = 2xy–x² -…

A: The given function is  f(x,y)=2xy-x2-2y2+3x+4.

Q: Consider the function f(x) = x + 2/x − 6 . a) Is the point (3, 14) on the graph of f? b) If f(x) =…

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Q: Find the Fourier series expansion of the periodic ʻramp' function f(x)= 2x, valid between x = 0 and…

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Q: Given 7 f(x) dx = –10 f(x) dx = 8 %3| 7 6. g(x) dx = –1 g(x) dx = -8, compute the following…

A: Given problem:-

Q: Find the center of the circle x ^ 2 + y ^ 2 - 6x + 4y - 23 = 0

A: find the center of circle if it is helpful, please thumbs up or appericiate.

Q: Let f(x) = 2x + 3/3x-2 , g(x) = 4x/3x − 2, h(x) = √3x − 12, F(x) = 3x + 4, G(x) = 2x − 3 a) Find the…

A: Solve question

Q: On a sketch of y= e*, represent the left Riemann sum with n = 2 approximating ff e dx. Write out the…

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Q: Given y = Vx – 2Va – 2; Find y'. - |

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Q: xト10 (オー2)(xフxt) dx

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Q: Find the number of 3-permutations of a set with seven elements. a. 130 b. 120 c. 210 d. 100

A: The number of r-permutations of a set with n elements= P(n,r).

Q: 6) Find the resulting function after the following transformations are applied to the graph of h(x):…

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Q: Write the integral in terms of u and du. Then evaluate. (8х + 19)-2 dx, и 3D 8х + 19 (Use symbolic…

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Q: Write the integral in terms of u and du. Then evaluate. x(x + 1)5 dx, u = x + 1 (Use symbolic…

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Q: Problem #6: Consider the following function. H(x, y) = 7 In(3x² +y³) %3D (a) Find f(2,3). (b) Find…

A: a. fxx(2,3)  = 42(-3×22+32)(3×22+32)2fxx(2,3)  = -0.2857

Q: 5x +2y -9z 44 -9x -2y +2z 11 6x +7y +3z =5

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Q: dx 5. S- (4x – x2)°/2

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: The population A (in thousands) of Atlantic City in 2014 was 39,521. In 2018, the population was…

A: The population A in thousands of Atlantic City in 2014 was 39,521. In 2018, the population was…

Q: Write the system of equations that corresponds to the following augmented matrix. 1-9 9. -3 5-4…

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Q: Solve the following differential equations of 1– y' = 2y – x; 2-x'y'y'+

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Q: 4. If ) Cn (x + 2)" converges for -5 < x < 1, find the radius of convergence of the series. n=1

A: ∑n=1∞cn(x+2)n Since series convergence for -5&lt;x≤1Then Interval of convergence is (-5,1]Let R be…

Q: Q-5: [5 marks] Find the points at which f(x) = (x – 2)*(x + 1)³ has relative extrema.

A: Solving extreme