Using vector Calculus, Parametrize the circle of radius 5 having centre (8; -3) and hence and a tangent vector and the tangent line to this circle at the point (5; 1).

Q: 2 0 1 8] 5 6 0.5 3 [20 A = |-5 [24 12 -36] 10 -30] 5 [2] B = |1 C = [0 8 4] D 2 1 2 4 Lo] -3 7 –1 0]...

A: Please find attachment for the details solution 

Q: 3t Find the general solution of the differential equation: y+ 5y= te Use lower case c for the consta...

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Q: 1. Find the volume of the solid that lies within both the cylinder a2 + y? = 25 and the sphere x² + ...

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Q: Which of the following is NOT a function? a. A = {(1, 4), (3, 5), (1, —5), (3 , —5), (1, 5)} b. A = ...

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Q: Problems 1-3: always necessarily true. If possible, provide an example to support your statements. B...

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Q: Sæ' = (2 – x)(y – x) y' = y – 2x – 2 - The system can be linearized at the critical point (-2,-2) to...

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Q: Find the Fourier transform of f(t) defined by: t < 0 t 20 f(t) = e-6t

A: We know that the Fourier transformation of a function fx is  fs=12π∫-∞∞eisxfxdx

Q: VI. Give the Maclaurin series expansion of f(x) = ln(2 – 3a). Determine its interval of convergence....

A: Given: f(x)=ln(2-3x) To find: Maclaurin series expansion of given function and ln(0.5) using 5 terms...

Q: dy Solve the initial value problem dt + 4t + 4t , y(1) = – 1 %3D t+1 y(t) = Question Help: Video M M...

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Q: In this exercise, we suggest the use of technology. Round all answers to two decimal places. Maximiz...

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Q: 4. Use Laplace transforms to solve the following initial value problems. d?x "+2+4x = 0, x(0)=0 , x'...

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Q: Adams School orders 3 cartons of chocolate milk for every 7 students. If there are 581 students in t...

A: Please find attachment for the details solution 

Q: Proposition 9. Let n be a non-negative integer. Then 1+2+4+ 8+ ..+ 2" = 2"+1 – 1. Special directions...

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Q: dy Find the general solution of the differential equation: dt 41. Use lower case c for constant in a...

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Q: Dylan wants to accumulate at least $60,000 by depositing $1,400 at the end of every month into a fun...

A: Dylan is depositing $1400 per month to get $60000 where interest is compounded monthly formulae for ...

Q: Proposition 6. Consider the function g : Z? → Z² defined by g(m, n) = (m – n, n – 2m). The function ...

A: To show that a function f is bijective, we have to show that it is one one and onto.  Again we know ...

Q: 900x50

A: Given that  900 × 500

Q: 1. Let x E Z. Prove that if x4–1 is not divisible by 4, then x2 – 4.x– 3 is also not divisible by 4.

A: As per our guidelines we are supposed to answer only one question.   So, here is the ques. no. 1

Q: 13. Encrypt the plaintext message GOLD MEDAL using the RSA algorithm with key (2561,3).

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Q: Determine the laplace of the following functions. 1. f(t)=[sin(2t)]^2 2. f(t)=e^(5t)(t^3) 3. f(t)...

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Q: Proposition 13. For integers n > 1, 1 2 3 n 1 1 - - - 2! 3! 4! (n + 1)! (n +1)!" Hint: Try induction...

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Q: . Suit Sales The number of suits sold per day at a retail store is shown in the table, with the corr...

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Q: For what values of h are the given vectors linearly independent? -10 3 h Vectors are linearly depend...

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Q: dy Solve the separable differential equation dt t?y + y Use the following initial condition: y(0)= 5...

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Q: Plot the point that has the given polar coordinates. (-5, 0) A/2 л/2 4 -2 T/2 л/2 Give two other pol...

A: Given: Polar coordinate -5, 0. To plot: The given polar coordinate. To given: Other polar coordinate...

Q: Consider the initial value problem, (6z – ly)y' = (x – 8) o + 2, y(z0) = y0 If ro - 7, then for what...

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Q: 1. Let A be a nonempty subset of R and let a E R. Show that if there exists a sequence {a,,}1 such t...

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Q: 6. When finding the determinant using cofactor expansion, it is necessary to select the row or colum...

A: As per Bartleby guidelines we're supported to answer only first three subparts. Kindly repost rest.

Q: lim yz? (2, y)(0,0) along y = 2x? %3D O does not exist 1/2 215

A: We have to find  limx,y→0,0yx2x4+y2 along y=2x2

Q: The sum of nine times a number and 2 more than the number is the same as the difference between - 10...

A: Suppose that the number is x,  Now sum of 9 times that number and 2 more that number = 9x+x+2 Again ...

Q: 7x2. 7xy ly' = 48y – by² – 8xy 49x | - The critical point not on the axes is a(n) Select an answer S...

A: Solution

Q: s - 3s2 – 2 S .3 s° + s

A: It is known that:  L-1as2+a2=sinat L-1ss2+a2=cosat L-11s=1

Q: If z = x2 + y?, x = e' cos(s) and y = e' sin(s), then %3D dz at (t, s) = (1,0) is as %3D

A: Given that z=x2+y2, x=etcoss and y=etsins First we have to find ∂z∂s.

Q: Prove. Power set of a null set is empty.

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Q: +oo +oo n² – 1 n2 +1 (-1)" (a) Σ (c) )un where sn = u1 +... + un = n! n=1 n=1 +oo 1 - 11 n=1

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Q: 18.12. Let the function f be entire and f(z) → o as z 0o. Show that f must have at least one zero.

A: We are given that f be entire and f(z) goes to infinity as z →∞  and we  have show that f has at lea...

Q: The graph below represent the domain of the function O f(r, y) In(1 -+y) Of(r, y, z) = VI+y-1 Of (r,...

A: The given graph represents x+y&gt;1. The domain of ln(1-x+y) is 1-x+y&gt;0⇒-x+y&gt;-1⇒x-y&lt;1. So t...

Q: Let = axty + bx°y", with a and b constant. Pis a point given by (1, -1) and it is known that (P) = 3...

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Q: +0o In n E(-1)" n2 n=2

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Q: True of False Choose True if the statement is correct, otherwise False. 1. Suppose a matrix A has th...

A: 1.Let us consider a matrix:A=123111001Now,detA=123111001=1[1-2]=-1

Q: The goal of this problem is to justify the following statement by using the Comparison Test for seri...

A: To prove the given statement using the comparison test.

Q: Calculate the determinant of 2x² + 3X + 5 O 23931 O 13249 O 12394 O 23419

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Q: correct answer for all parts

A: Zeros of the polynomial

Q: Determine the particular solution that satisfies the differential equation and initial condition bel...

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Q: [x² when x # 1 9: Show that f(x) = %3D 2 when x =1 is discontinuous at x = 3D1

A: The given function is: f(x)=x2when x≠12when x=1We have to show that the given function is discontinu...

Q: 8. Describe the transformations on the given logarithmic function. g(x) =-{log 1,[- ¿(x- 7)]– 85

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Q: 48. Let f be a function defined on ]0, 1[ by : 0, if x is irrațional f (x) = {1/q, if x=p/q; where p...

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Q: 7. Check if the following graphs G and H are isomorphic. G: H:

A: Given the graphs G and H below.

Q: y У — х. y' = 2+ sin

A: Given y' = yx + siny-xx    ---(1)