dt b) + 5y = 2, y(0) = 0 dt c) 3+y = 2, y(0) = 0 dt d²y dy d) 4, y'(0) = y(0) = 0 dt2 dt

Q: 7くt<12 t.

A:

Q: Let I = {(x, y) |1, y E 2Z}. (a) Show that I is an ideal of Z × 2Z. (b) Use FIT for rings to show (Z…

A: We will show both parts.

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Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

A:

Q: 6. On a certain day, the depth of water off a pier at high tide was 6 m. After 6 h, the depth of…

A:

Q: III. Find the parametric equations of normal line to the surface given by f(x, y) = tan V x² + y² at…

A: Given : The equation of the given surface is,   f(x, y) = tanx2+y2 To find : We have to find the…

Q: R is The lowey timit topolygy Pimer than the strmdard topoleoy てom

A: The given question is related with topology. Let Τ' be the lower limit topology on ℝ and Τ be the…

Q: Determine if the columns of the matrix form a linearly independent set. 1 4 -3 0 -2 -7 5 1 -4 -5 7 5…

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Q: 1 - x 1 2 - y = z +1 and l2 : х — Consider the lines l1 : = y – 2 = 3 || 2.

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Q: 16) roțațion 90° counterclockwise about origin Find the cordinates of the vertices of each tiquse…

A: Let us perform the given transformations.

Q: Find the standard equation of the sphere. (Let r = 5 and C = (9, 7, 5).)

A: Standard equation of a sphere with radius r and centre at c=(h,k,l) is  (x-h)2+(y-k)2+(z-l)2=r2

Q: Solve by the Laplace transform, showing the details and graphing the solution: 35. yí = 2y1 – 4y2,…

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Q: Suppose that for a company manufacturing bluetooth and wireless headsets, the cost and revenue…

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Q: (a) Evaluate the integral using integration by parts rule if x' cos' 2x dx (b) Express the…

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Q: Find the values of w, x, y, z and Dx x + y + z + w = 13 2x + 3y - w = -1 -3x + 4y + z + 2w = 10…

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Q: Evaluate the integral using Simpson's 1/3 and Simpson's 3/8 with n%3D11. Express the answer in four…

A: Simpson's 13 rule: We need to evaluate ∫14x-1 dx with n=11 Now, h=b-an We have a=1, b=4, n=11 So,…

Q: іa + (2 — i)234- 3і (1+ i)x – x2 = -3 – i |

A: The solution is given as

Q: a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to…

A: We have to find the followings ; (a) We have to find the coordinate vector of  q(t) = 4t2+2t+9 with…

Q: Consider the function g defined by 1 g(x, y) = sin (TVry) + log3(x – 3y) Do as indicated. 1.…

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Q: (a) Find the Taylor's series for the function f(x)= sin x at x = (b) Using L'Hospital 'rule to find…

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Q: 3. Solve for x: 4 Ox = 13.5 O x= 2.7 O x=9 X = Ox= 6

A: Introduction: The chord of a circle is the line phase that connects any two locations on the…

Q: -2 3 11 4 5 -3 4 -2

A: We need to find the Determinant.  Now, consider:…

Q: 0. F A particie moves along a norizontal line. Its position function is s(t) problem, find the…

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

Q: Show, using truth tables, that (a) ¬(p V q) A r = -p^ (¬q ^ r), (b) -4 v (q V p) is a tautology.

A: (a) To show ¬p∨q∧r≡¬p∧¬q∧r using Truth tables. (b) To show ¬q∨q∨p is a tautology using Truth tables.

Q: 2s – 10 -5s

A: We have to solve given problems:

Q: The value of the triple integral 2x dV E where E is the region inside both x? + y? + z? = 36 and…

A: Solution:-

Q: Let W = {(" ) :a + 2c = 0 and b-d = 0} be a subspace of M2.2. Then dimension of W is equal to: O 4 O…

A: Dimensions of the subspace of a vector space

Q: Let M = {(, ¿ )-G i )G : DC : D Then M is a basis for M2,3 the above M3,2 the above O None of the…

A: Given that     M=110000, 110010, 100101, 100001

Q: Section A : Solve the boundary value problem d²y = x+ 2y, with the boundary conditions dx² Y(0)=0…

A:

Q: 27TT 5. x = y? and x + y = 2 is revolved about y = 1. (Answer: с. и. ) %3D 2

A:

Q: graphing the solution: 36. yi 3 2y1 + 4у2, у2 —D у1 + 2у2, У1(0) 3 — 4, У2(0) %3D — 4

A:

Q: Determine whether the Fourier series of the following functions converge uniformly or not. a) f(x) =…

A: The function given is as follows: fx=sinhx,    -π&lt;x&lt;π We are asked to find the Fourier series…

Q: 1. Let V (x, y) 1+ x2 + y 1+x² + y* and let F(t) = x(t)î + y(t)ĵ where cos(t) (cos (t) + cos²(t)(2…

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Q: Example 2 If |z-= 2, then the difference between max (zl) and min (|zl) is: (A) 1 (B) 2 (C) 4 (D) 8

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Q: 3. 2 B -1 0 1 а) A = 1 -2 -4 5 -3 -3 b) A = 7 11 -11 13 A 28 43 -6 18 B = 22 -3 c) 3 7 4 3 12 B = d)…

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Q: dy - y = x² sin x . Solve X dx

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Q: Which of the following statements is false? O A. Elementary row operations do not change the row…

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Q: Find the area of the region R = (x, y) such that |x-1|-|y+1|<1 |x-1|+|y|<1

A: We will find all inequation eliminating modulus and the find common region bounded by both in…

Q: what about part 5)?

A: Please find the answer innext step

Q: Find the two-term perturbation approximation to y" = e", y(0) = 0, (0) = 0. %3D

A: Given:                                    y"= e∈y                               y(0) = 0…

Q: †3 – 12 +5t + 2

A: Laplace transformation of polynomial

Q: Given the differential equation dy _ (4x + y)(x +y) dx x > 0. x2 a) Find the general solution of the…

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Q: The series 2 (-2)" is n=1 n4" +1 Absolutley convergent Conditionaly convergent O Divergent O None of…

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Q: tind the remaininn parts of the spherical trinngles 95 09' 7" C 79°18'29", C= 900

A: Given: a=95°09'17''c=79°18'29°C=90° To find: Parts of spherical triangle

Q: •MMD1:ro AV% Then M is a basis for M2,3 O the above M3,2 O the above O None of the mentioned

A:

Q: Find the determinant of the following: 2 0 41 1. I. -2 3 4 -3 4 1 1 2 4 L4 4 2] 4. 5 -2 5 4 61 2. -1…

A: We have to find determinants of give matrix.

Q: Let V be a vector space of dimension 4, and let W be a vector space of dimension 2. Let L:VW be a…

A:

Q: Final Answer for a1,a2,and az a, =S° - -1dx +- " 1dx = ? 2n-T 2n (1)()(x) 1 | 1 cos- (1)(1)(x) a1 -1…

A:

Q: 4- Calculate the substitution using SSm y dxdy -if the set M is given by inequalities x² + y° < 4x,…

A: We have x2+y2≤4x⇒x2-4x+4-4 +y2≤0⇒(x-2)2+y2 ≤4⇒(x-2)2+y2 ≤22    ( represent the region inside the…

Q: Prove that if g′ is bounded on (a, b) then g is uniformly continuous on (a, b).

A: