There are 5 posts that are EQUALLY placed end to end on every side of a regular octagon. How many posts are there in all to enclosed the octagon?

Q: Let Bt be 2-dimensional Brownian motion and put Dp = {x € R²; || 0. Compute p⁰[B₁ € D₂].

A: Given: Bt is a 2-dimensional Brownian motion           Dρ=x∈R2;x<ρ for ρ>0To find: P0Bt∈Dρ=?

Q: If blocks A and B of mass 10 kg and 6 kg, respectively, are placed on the incline and released,…

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Q: This question concerns the linear system of differential equations dx dt dy dt = kx + (k² + k)y = x…

A: Given system of equations                               dxdt=kx+k2+ky…

Q: One card is randomly selected from a deck of cards. Find the odds in favor of drawing a red card.…

A: Solution: Given, one card is randomly selected from deck of cards.  We have to find odds in favor of…

Q: 4. If u is harmonic, show that in terms of polar coordinates J²u ди 7.²0²u +r- + Ər² Ər 20² (hint:…

A: Convert the Laplce equation into polar coordinates.

Q: Are the following statements true or false? Either prove the statement is true or provide a…

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Q: f d a h с 6.0 g e b

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Q: Let X; be independent Uniform(-7,7) random variables, for i=1, 2, ..., 7. Let Y=X₁+X₂+...+X7. (b)…

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Q: Find the volume of the solid that lies inside both the cylinder x² + y² = 25 and the sphere x² + y²…

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Q: 9. P = $9000, r = 6.75%, t = 4 months

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Q: The product of two consecutive positive integers is always even. Then, the product of 11 and 12 is…

A: The product of two numbers is even if atleast of them is even.  In two consecutive positive integers…

Q: max -(x₁ - 4)² – (x₂ − 4)² 11,72 x₁ + x2 ≤ 4,21 + 3x2 ≤9

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Q: Find the centroid of the lamina bounded by the x- and y-axes, the line x = 2, and the graph of y =…

A: What is Centroid: The centroid of a three-dimensional solid or a two-dimensional planar lamina…

Q: Find an equation in rectangular coordinates for the spherical equation = 2 csc(o)sec(0)

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Q: f1 does not equal e- 2t and f2 does not equal e - 6t

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Q: Find the circumference and area of the adjacent circle. Use the key for The circumference of the…

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Q: Find the least squares solution of the system Ax = b. 1 1 H 1 2 2 1 X = A = ↓ 1 b 3 99] -2

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Q: Set up a triple integral in cylindrical coordinates for the volume of the solid region E, where E is…

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Q: Given Conic Equation 2 9x² - 44² +548 +164 +29

A: Introduction: One of the key concepts in geometry is conic sections. The angle generated between the…

Q: If f(x) = 7x-2 and g(x) = 4x - x2, determine the following: a. f(x) o g(x) Answer (a):

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Q: Let E be the region bounded above by x² + y² + z² = 10², within x² + y² = 3², below by the xy plane.…

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Q: 3. Let f(x) [1,00) and = for all x ≥ 1. Show that ƒ is integrable on the interval √ 1₁²01 = 2 = ²³²…

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Q: Let f(x) = sin(2x) and let [a, b] = [0, 1]. = (a) Construct a piecewise-linear polynomial that…

A: The function given is as follows: fx=sin2πx on the interval a, b=0, 1. (a) We are asked to find the…

Q: Consider the following where the principal P is invested at an interest rate of r per year for t…

A: To find the accumulated amount of the given investments.

Q: Prove the following. 1. The sum of four consecutive integers is even.

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Q: 10. matrix Let 01, 02, 03 be the Pauli spin matrices. Is the 4 x 4 (14-01) 1-01001-02 002-03 003) =…

A: Given: σ1,σ2,σ3 are the Pauli spin matrices.We need to check whether the 4×4 matrix…

Q: A man is walking at a rate of 6 miles per hour towards the foot of a tower, 80 feet high. At what…

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Q: Let f: R2R where f(x, y) = x² + y² if both x and y are rational and f(x, y) = 0 otherwise. Prove…

A: Let function f:ℝ2→ℝ defined such that, f(x, y)=x2+y2,x, y∈ℚ0,otherwise To prove that Df0, 0 exists.…

Q: Let W be the set of all vectors of the form shown on the right, where a, b, and c represent…

A: I have given the answer in the next step. Hope you understand that

Q: Find the projection of v onto u.

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Q: If f(x) = 7x-2 and g(x) = 4x - x2, determine the following: a. f(x) o g(x)

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Q: Find a unit vector orthogonal to both u and v. u = −5i + 3j - 2k 11-31+ 1 j+_¹_k 10 V =

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Q: Determine whether the set S spans R2. If the set does not span R2, then give a geometric description…

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Q: 40. YA 3 2. 0 y = f(x) 2 +3

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Q: In GHI below, GI is 3.5 m and G is 33°. Determine the length of GH to the nearest tenth of a…

A: first see note for just reference.  problem1 , final answer is GH = 2.9 meters

Q: 1. Given U={x|xEZ,5≤x≤20) and its three subsets: A={alaEU,a is even), B={b]bEU, b=10), C = {c | CEU,…

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Q: Let A = [55];m € R; [1 B = 0 Lo 3 -1 0 [2 1 0 L2 -1] -3 7711:0=121 a) Find CTC -3A, if possible. b)…

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Q: 4. A = [! -6 4 07 020 %]

A: Nul( A) i.e null space of A

Q: Show that the given function is a solution of the differential equation. dy dx dy dx || +9y = e-9x .…

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Q: 830 52° USE SOH CANTO A X FIND X 830 3m E 3m FIND X yo 38°

A: For any right triangle, using SOHCAHTOA, it can be written that:…

Q: Graph the curve given by the equation r=2-3 cos(0). Label the exact polar coordinates of at least…

A: Given polar equation is r=2-3cosθ . To Plot : 1) The graph of the given equation. 2) Label the three…

Q: use some form of technology to determine the eigenvalues and a basis for each eigenspace of the…

A: A number λ is said to be an eigenvalue of the matrix A if there exists a non-zero vector x such that…

Q: 10. a b C d a + 3b = c b+c+a=d

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Q: 4). For the sequence, determine if the divergence test applies and either state that lim n→∞ an does…

A: Concept: Divergence test: The nth term for Divergence states that if   then the series  is…

Q: Derive the Laplace transform for the following time functions: a. u(t) b. tu(t) C. sin wt u(t)

A: We have to find the laplace transform of the given time functions.   According to guidelines we…

Q: Find the surface area of the surface given by the portion of the paraboloid z = x² + y² that lies…

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Q: Verify that f(z)=tanh(z) is a periodic function with period лi (z is a complex number)

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Q: - [B 3. A = 935 14 -2

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Q: 7π 4 decimals to at least one decimal place. Convert the point (r, 0, z) (x, y, z): = = 6, " to…

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Q: Find the orthogonal complement W⊥ of W and give a basis for W ⊥

A: If W is a subspace of a vector space V then, the orthogonal complement of W is the subspace W⊥ given…