Graph the two equations f(x)= 0.1x^2+0.5 g(x)= -0.1x^3+4x and find the volume if the cross sections perpendicular to the x-axis that are equilateral triangles

Q: Show that if gcd (a, y) = 1 and a \xy Then a \x

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Q: y = 8x - x² P (5, 15) (8,0) X Figure 2 Figure 2 shows the curve y = 8x - x² and line I which is a…

A: It is given that the line l is tangent to the curve y=8x-x2 at P5,15. The curve intersects the…

Q: sketch a graph of the region bounded by the graphs of the equations. Then use a double integral to…

A: sketch a graph of the region bounded by the graphs of the equations. Then use a double integral to…

Q: If the vector v has initial point P, what is its terminal point? v = (0, 0, 3), P(0, 1, -3) (x, y,…

A: Given: v=0, 0, 3, P0, 1, -3. Also, P is the initial point of the vector v. We have to find the…

Q: Solve the initial value problem The solution is x(t)= 1 4 4t +=e + 1/4 - 12/²1 −2+t+2e¯t + te-t 9 -e…

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Q: The vectors V₁ 3 -9 and V₂ = 6 9 2 15 2 form an 9 orthogonal basis for W. Find an orthonormal basis…

A: Given: Vectors, v1=3-96, v2=921529 form an orthogonal basis for W.To find: The orthonormal basis for…

Q: Does (7, 0) make the equation y = 2x + 7 true?

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Q: Given that a connected graph G has diameter d, state (but do not prove) the lower bound for the…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: 2. Find a Fourier series particular solution for nonhomogeneous vibration equation where the…

A: Given: Vibration equation, d2udt2+u=Ft. The graph of Ft is as follows-To find: Fourier series…

Q: Given: f(x) = (x²,0 < x < 1) (π, -1 ≤ x < 0) a) Find the FOURIER SERIES of the given STEP FUNCTION.…

A: Given function is: fx=π,        -1≤x≤0x2,           0≤x≤1 (a) The fourier series is:…

Q: Alice, Ben and Carl collect stamps. They exchange stamps among themselves according to the following…

A: Note: Due to Bartleby answering guidelines, I have solved only Exercise 1.

Q: Consider the system of equations shown below. 3w 2x + 16y - 2z = -9 -W + 5x 14y + 18z = 23 3wx+14y +…

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Q: An observation indicates that the initial population of grey seals P(t) nearby a harbor is 25 and…

A: The grey seal P(t) is defined as: dPdt=0.0225P(t) - 0.0003P(t)2 = f(t, P)with P(0) = 25Therefore,…

Q: Suppose that f(0.25) = f(0.75)= B. If the Composite Trapezoidal rule with n = 2 gives the value 4…

A: Solution :-

Q: Solve the integral. dx S √1 - 4e²x

A: Using some formulas in question  as logmn=logm-logn and,∫1x2-a2dx=logx+x2-a2+C where C is constant…

Q: The equation of line s is y=(5)/(7)x+8. Line t is parallel to line s   Solve asap in 2 min pls i…

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Q: With the function f(x) = x¹ + 3x³ - x² + 8 in the Cartesian plane below. Calculates the average rate…

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Q: Given that a connected graph G has diameter d, state (but do not prove) the lower bound for the…

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Q: 2. Test the following series for convergence. (a) 106n + con n + ain n Σ' 13 - 1 (11) Σsin (6) (c) Σ…

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Q: (c) Find the coordinates of point Q.

A: We have to find the coordinate of the point Q.

Q: Consider the following initial value problem.a. Find the approximations to y(0.2) and y(0.4) using…

A: Given: y't=4-y,  y0=3;   yt=4-e-t. To Do: (a) Find the approximations to y0.2  and  y0.4 using the…

Q: 2. Express as a single power series form: ²[₁ n=2 x2 n(n-1)anxn-2 + 00 n=0 anxn

A: Given that the power series x2∑n=2∞nn-1 anxn-2+∑n=0∞anxn

Q: a. Find the Euclidean distance between u → and v and the cosine of the angle between those vectors.…

A: As per our guideline, part a solved. Please repost the other questions as separate question.

Q: (a) Solve the following inhomogeneous wave equation on the real line Utt-c²Urr = 2x - sin r U(x, 0)…

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Q: Let G = Z16 .Find all automorphisms G. The group isomorphic with G and the #AutG group.

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Q: 6. Make a sketch of an object or explain the object that could be created using the pattern…

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Q: The number of non-negative integer solutions to the equation x + y +z+w = 15 is 816 680 1540 969

A: The general formula for the number of Non-negative integer solutions of standard problem form: x1 +…

Q: 3) Complete the following table. Characteristic Domain Range Does it have a max? Does it have a min?…

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Q: Use elementary row operations to solve the following system x+2y-z+3w = 4 2x+4y-2z+7w = 10…

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Q: Jse Residue Theorem to evaluate z ez dz, around the circle C |z| = 1 counterclockwise.

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Q: The rational zeros of f(x)=2x^(3)+3x^(2)- 8x+3 by using synthetic division.

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Q: If x1, x2 are the solutions of the equation = 1 496x+1, compute the value of x1 + x2). Select all…

A: Given, if x1, x2 are solution of the equation                               74x2=1496x+1.

Q: Consider the linear transformation T: RR represented by T(x)= Ax. Find the nullity and rank of T,…

A: The given matrices a) A=122101 b) A=110211010 c) A=120111132121 d) A=111211000 We have to find the…

Q: This question concerns the following exercise. Exercise Consider the linear transformation t: R³ R³…

A: t: ℝ3→ℝ3x,y,z↦2x,y+z,z-x

Q: Given a scalar-valued function of multiple variables, f(x) = x₁sin(x₂) + x²x3 + x₁x₂x3 + x3 -]. [X3]…

A: The given scalar- valued function is fx=x1 sinx2+x22 x3+x1x2x3+x3where x=x1x2x3.The quadratic…

Q: IV. Consider the primal LP below. subject to: Max z 3x1 + 2x2 4x1 - 3x2 ≤ 6 x1 + x₂ ≤ 5 X1, X20

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Q: Look at the graph in the file Q2Kruskal.pdf. It shows locations A, B, C, D, E, F and the edges show…

A: The given graph is as follows: A minimal spanning tree is a subgraph that covers all the vertices…

Q: – ^= { #² = 1 MEN=41}\ A : n n N, n‡: }. n³ Let B be a bounded from above subset of R. Prove that -B…

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Q: Find the minimum and maximum points of on the sphere f(x, y, z) = 2x - 4y + 4z + 10. x² + y² + x² =…

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Q: a) An integral is given as fo f(x)dx = c where a, b, and c are positive constants. What is the value…

A: We have to answer given Questions.

Q: A particle moves long the x-axis so that its velocity v at any time t, for 0 ≤ t ≤ 18 is given by v…

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Q: i Let A = [₁ + i ₁₁ ], B = [₁²; ₁²d- A. 8 B. -8 C. 8i . Then det (AB) = D. -8i E. 4i

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Q: 8²y 0²= 250²2; 0 0 ду at² Using the www wwwww decomposition method, solve the equation for the…

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Q: Find the directional derivative of ƒ (x, y, z) = 6 xy² – 4yz² — z² at P = (3, 2, -4) in the…

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Q: The 5th term of an arithmetic series is 12 and the 11th term is 60. (a) Find the first term and the…

A: (b)                 Formula :   nth term of an arithmetic series with first term a and common…

Q: 1. Consider the Surface S₁ with equation x² – 4 = 2z • Draw and sketch the graph of S₁ in R³.…

A: The surface S1 with equation x2-4=2z. To draw the surface S1 in ℝ3.

Q: | Find all the poles of poles of 1 f(z) = ₂1² f(z) z3-1 and their residues.

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Q: 2 of,x²-x-1=0 a" - fn a-B a, ß are roots (a>ß) and, t = n (n≤N), if, b₁=1, b = = t n n-1 (n ≥2) find…

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Q: PRACTICE EXERCISE ON DETERMINATION OF INTEGRATING FACTOR 4. y(8x-9y)dx+2x(x-3y)dy = 0

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Q: Uniform shaft is fixed at one end and free in other end, if 020 0x2 t>0 (0.0) 020 д12 0(0, 1) = 0,…

A: Given: ∂2θ∂t2=a2∂2θ∂x2, 0&lt;x&lt;1, t&gt;0 with the initial conditions.To find: The angular…