calculation for P.I ур cos²x b²+1 2 cos²x D² + 1 + {² 22{ -} 1+ cos2x D² + 1 HOW DID HE GET THE VALUE INSIDE THE CIRCLE

Q: 9. C wants to see all eight directions, he travels clockwise and he moves from one direction to…

A: Given: C wants to see all eight directions. He travels clockwise and he moves from one direction to…

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Q: In Problems 4-6, find the steady-state solution. 4. U = a 2u,, 00 u(p, 1) = 0

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 12. Verify by direct substitution that Un(x, y) = sin nx sinh ny is a solution of Uxx + Uyy 0 for…

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Q: Fed braically, all roots (Intercepts) of the equation 1(2)=62¹-8²-342² +12z

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Q: Question 18 0<0<27, calculate the value of

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Q: 6. Determine the Fourier integral representation of the following: 0 < t < 1 elsewhere t, f(t) = {t

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: Here given function as fx=2x+7 , x∈0, 2, 4 rectangles Now ∆x=2-04=24=12 Thus, four sub-intervals for…

Q: At what values of x does the graphs intersect? F(x)= x^3+x^2 +7x+1 G(x)= x^2+7x

A: We need to find the values of x at which the graphs F(x)= x^3+x^2 +7x+1 and  G(x)= x^2+7x intersect.

Q: Question 3 i) Using the Cartesian position vector r, show that V (0)²³ + |||| ii) Consider some…

A: Here  (i) we have to show that ∇1rk=-krrk+2 (ii) Given u=x+my, v=mx-y  (iii) Given fx,y,z=xyz and…

Q: iii) Confirm your total flux calculation by computing the surface integral 2 > - #f. x-nds - Σ //₂²…

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Q: We learned how to construct the map ² (V) → VV that sends the simple wedge V₁ V₂ → V₁ V₂ V₂ V₁ -…

A: Given that the map Λ2V→V⊗V is defined by the function, v1 Λ v2→v1⊗v2-v2⊗v1 We are asked to prove…

Q: 3x + 4y = 8, 4y - 3x = 8, 4y - x² = 1. Sketch of the region D and describe its symmetry. Find the…

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Q: State the domain and range of the following function: ƒ(x) = ²log((−4(x − 12)) + 3 domain {x € R/x…

A: Domain and range of the function

Q: Question 6 A vector field is given by F(r) = zî+x+yk, and a paraboloid is given by S = {(x, y, z)…

A: The given vector filed is F(r)=zi^+xj^+yk^. and the given surface is a paraboloid…

Q: Needed

A: We solve given ODE.

Q: Find the maximum and minimum of Q(x) = x² + x1x2 + 3x2x1 + x² subject to |||| = 2 along with the…

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Q: Solve the following CDES by variation of parameters method: y" + 5y' + 4y = x²e²x

A: Here given the differential equation as y''+5y'+4y=x2e2x or D2+5D+4y=x2e2x ........(1) The auxiliary…

Q: The graph of y = log6(216x) can be obtained by stretching or translating the graph of y = log6x. A)…

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Q: Find the disjunctive normal forms of the left-hand side and right-hand side of the following…

A: (i) A disjunctive normal form for m is a sum of product. Consider the given equation,  x⊕yz = x⊕yx⊕z…

Q: 3) How many arrangements are there of the letters in the word Neutrogena?

A: Sol

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT ſ(−12xy² + 8x³y + 3)dxdy

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Q: Determine the interval in which solutions are sure to exist. y(4) + 8y" + 5y = t Valid on the…

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Q: Consider the subspace of M22 defined by V T(p) by = [PO p(0)] p(0)] = = { [8 a]: a,b € R}, a ER, and…

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Q: ● By power series method, Solve the following ODES & C₂ x² e² + 2X =-2 X-2X Ans: Y = C₂ X e + 2 X…

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Q: Show that xp-yq=z and x^2p+q=xz are compatible and solve them

A: Given   :   xp-yq =z and  x2p+q =xz To find : Solution of Differential equation

Q: A coffee manufacturer is interested in blending five types of coffee beans into a fine blend of…

A: a. Let number of pounds of component 1,2,3,4,5 be x1,x2,x3,x4,x5 Total blend weighs 120,000 pounds.…

Q: A function of period 2L has the form f(x) = L²x², xe [-L, L]. i) Compute the Fourier series for this…

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Q: Let {₁,..., wk, Wk+1,...,n} be a basis of R" and c₁,...,CER be nonzero scalars. (a) Prove that S =…

A: Note that we used one fact in this prove which state that if B is basis of V and C is any linearly…

Q: Why we say lie to our own self

A: question- why we say lie to our self? answer 1) To avoid getting punishment. 2) To project another…

Q: (a) y' = = ing 3t²y y+1' are probler y(2) = 1 biems

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Q: A spherical vector field is given by F(r,0,0)=2r cos(0) êr + 3r sin(0) ê +0(π- 0) ê. i) Compute the…

A: It is given that Fr,θ,ϕ=2rcosθe^r+3rsinθe^θ+θπ-θe^ϕ. Thus, F1=2rcosθ, F2=3rsinθ, and F3=θπ-θ.

Q: 2. (a) Given a point ro and stepsize h, use Lagrange polynomials to find the quadratic polynomial…

A: Solution a: Given points are x0-2h, x0 and x0+h Since we know the formula for Lagrange's…

Q: 7) Express 55C13+55C₁4 as a single term from Pascal's triangle.

A: 8

Q: Q.5 Solve the wave equation: U₁=Uxx-ex-6x, U(0,1)=8, Ux(1,1)=3, U(x,0)=4sin ³x+ex+x³-ex+7 **********

A: Using separation of variables

Q: An undamped mass spring system is modeled by the differential equation y" + 100y = 0 a) Convert the…

A: a. Given differential equation is y''+100y=0 Let x1=yx2=y'=x1' So, x2'=y''=-100y=-100x1+0x2 So, the…

Q: Let A = (a, a, as) and B = {b₁,b₂, b3} be bases for V, and let P = {[b₁]A, [b₂]A, [b3]A} (are)…

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Q: el (a type of fish). Al the population declin

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Q: 3- y" - 2y3y = -3te-t

A: This is a non homogeneous differential equation. We solve the equation for homogeneous part then…

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Q: Consider the family of curves: y² - 2x² = cy. A) Describe this family geometrically (e.g., "circles…

A: It is provided that: y2-2x2=cy. We need to describe this family geometrically. We also need to…

Q: 2) Solve for x (give your answer as an integer between 0 and 9): 51 + 27 ≡ x(mod10)

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Q: Find the general solution to the equation y(4) - 16y" + 64y" = 0. NOTE: Use C₁, C2, C3, and c4 as…

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Q: (a) F(s) = 2s (s¹ +24s² +144)

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: 2 Solve the following ODES by Inverse Operator method 2X (D-1) y = 2 sinhx + sinx -X Ans: y=c₁e +₂e…

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Q: 2. For each graph, identify a) the coordinates of the vertex b) the equation of the axis of symmetry…

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Q: Use the greedy algorithm to make change using quarters, dimes, nickels, and pennies for 5100 rupees

A: It is known that 1 quarter = 25 cents, 1 dime = 10 cents, 1 nickel = 5 cents, 1 penny = 1cent. Also,…