Use the Laplace transform to solve the given integral equation. t ['sind f(t) = 3t - 9 sin(t) f(tt) dr

Q: Use Weiestrass's definition of limit to show that lim (7x - 3)= 32. x-5

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Q: Let A E R have eigenvalues A₁,..., A. Prove that ker(A-AI)= ker((A-AI)2) for each i = 1,...,k if and…

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Q: 2) Find what conditions must be placed on b, b, and b¸ in order for the 1' 2' following linear…

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Q: For any integer z, if 3 divides z2, then 3 also divides z.

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Q: f G is a group and H is a subgroup of ind how that H is a normal subgroup of G.

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Q: (b) Do you think it is possible to change any other numbers in the first three rows of A such that…

A: Please find the attached answer

Q: (a) Show that S is path-connected, by constructing for any two points x, y € Sn an explicit path…

A: please find the attached solution

Q: If G is a group and H is a subgroup of index 2 in how that H is a normal subgroup of G.

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Q: How many three-digit numbers are there?

A: The count of three-digit numbers are determined as shown below.

Q: Find the shortest dist-mee between the limes y-2 3 and 2-1 2 x-2 3 2-3 ។ y-4 4 2-5 and also obtain…

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Q: At Mr. T's Delicate Donut Shoppe there are 5 flavors of donuts on the dollar menu. You have 35…

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Q: For the function f(x) = 1/16x​, construct and simplify the difference quotient f(x+h)−f(x)/h. The…

A: Given that,  f(x) = 116x Replace x by x+h , we get f(x+h) = 116(x+h) f(x+h) = 116x+16h

Q: Use sin + cos2 = 1 to verify the following identity: (a) tan² (x) + 1 = sec²(x) (b) tan(x)sin(x)=…

A: Introduction: Anytime trigonometric functions are used in an expression or equation, trigonometric…

Q: State A: - 6x + y = 11,600 State B: 141x+y=7,000 where x = 0 corresponds to the year 2000 and y is…

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Q: Problem 4. Let (X, dx) and (Y, dy) be metric spaces. Show that the sup norm metric do we defined on…

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Q: Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line…

A: ax+by+cz+1=0 →1It makes an angle 60° with the line x=y=z. So we get sin 60° = a+b+c3Σ a2 or…

Q: Consider the sequence (an) given by the recurrence an+1 = 2an-n for all n € N, with the initial…

A: We will find the pattern of a1,a2,.....,a6, the we can predict the general formula.

Q: (iv) d(u, v) (v) angle between u and v. (vi) proj,u

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Q: For the function f(x)=1/16x​, construct and simplify the difference quotient f(x+h)−f(x)/h.

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Q: (c) Find all zero of the rational function. (d)Use the information you obtain above, draw the graph…

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Q: Find the family of graphs G of order p such that y(G) = p.

A: Please find the attached solution

Q: 5.8. Let R = C[t]. Show that S = R[x]/((x)^(x, t)²) is not flat over R.

A: please find the attached answer

Q: John and Rosa want to retire in 10 years and can save $170 every 3 months. They plan to deposit the…

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Q: 2. If A is a 3 x 3 matrix, prove that the determinant of A is equal to the determinant of AT.

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Q: Given that f(x) = 3x + 1 and g(x) = x2 - 2x - 4, find (g * f)(6). (g * f)(6) =

A: Composite function value

Q: The initial size of a culture of bacteria is 1000. After 1 hour the bacteria count is 8000. If the…

A: In the give question to determine the time required for the bacteria to grow to 15000, first we have…

Q: Definition: Let V be a vector space and U₁, U₂, U be subspaces of V. Then V is said to be a direct…

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Q: Given: f(x)= = x³ x²-3' with f'(x) = x4-9x² (x² - 3)² and f"(x) = 62³ +54x (x² − 3)³ Make a table…

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Q: Solve the system below. -3x + 15y + X + 5y + The particular solution is: ☐☐☐☐ 00 y + + 5w = The…

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Q: Question 1 differential equation Consider the following 1 dy x² dx 2 + · y = x3 x5e-3x y-4

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Q: 3. What is the lowest degree of the polynomials that gives the value of A. P7(0.1). B. ps(0.1). C.…

A: Please find the attached answer

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. A…

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Q: Consider the u(x, y) = 2x - x³ + 3xy² function. Prove that it is a harmonic function and find its…

A: A function f(x,y) is harmonic is it satisfy fxx+fyy=0. The harmonic conjugate of the function is…

Q: Question 2 differential equation 1 = 1² + Consider the following 2 = 14e-41 y−3 a) Is the given…

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Q: Solve the following initial value problem: dx dt dy dt = = 3x - 4y 2x - y x(0) = 2, y (0) = -1

A: We will find eigenvalues and eigenvectors and then we wiil get the general solution.

Q: 4. Use the following Venn diagram for this question. P 67 8 r 4 q (a) List the regions of the Venn…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: ength of any edge of a regular tetrahedr ar tetrahedron). Show that the angle bet

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Q: Determine the pivot element in the simplex tableau. (If there is more than one correct pivot…

A: Given,

Q: Let W₁ and W2 be subspaces of some vector space such that the set-theoretic union W₁ U W₂ is also a…

A: Given that, W1,W2 be subspaces of a vector space V such that, W1∪W2 is also a subspace. To show:…

Q: Compute the inverse of f(x) = x³ + 1. f-¹(x) = ³√x-1 Check your answer by showing that ff¯¹(x)) = 3…

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Q: If

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Q: A certain amount of an indissoluble substance containing 2 kg of salt in its pores is subjected to…

A: As given , initial amount of salt S=2 kg. After 5 minutes, remaining amount of salt is 1 kg. Also,…

Q: OA, OB and OC, with O as the origin, are three mutually perpendicular lines whose direction cosines…

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Q: If the price of gold decreases at a monthly rate of 2.2%, by what percentage does it decrease in a…

A: Given  monthly rate of decrease =2.2% Let initially the price be p0 and the price after 12 month is…

Q: Solve equality: (a) 2x² + 3x - 2 = 0 (b) e¹+3e² 10 = 0 (c) ln(x) + ln(x + 1) = ln(12)

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Q: A company produces very unusual CD's for which the variable cost is $ 15 per CD and the fixed costs…

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Q: 3. If the eigenvalues of A are 5 and -1, with multiplicities 2 and 3, respectively, find the…

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Q: The following statements are made about (right) cosets of a subgroup H of a group G. Say whether…

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Q: Definition 3: Let X be a subspace of Rn and let X be the set of all vectors in R" that are…

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Q: Let a, b, c E Z and n E N. Assume a = b (mod n) and b = c (mod n). Prove that a = c (mod n).

A: Suppose a,b,c∈ℤ and n∈ℕ and assume that a≡bmod n and b≡cmod nTo Prove: a≡cmod n