3. Find the parametric equation of the line passing through the point (-1,0, 3) and in the direction N = (7,0,-2).

Q: Evaluate the given line integral. (y, -x) · dR, where C consists of the uppder part of 2² + y? = 1…

A:

Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: Find the Taylor polynomial of order 3 generated by f at a. f(x) = x2, a = 2 O A. P3(x) = 1 + 8(x –…

A:

Q: Consider the points which satisfy the equation y = x + ax + b mod p where a = 4, b = 2, and p = 11.…

A: Given : equation     y2≡x3+ax+b mod p where a=4, b=2, and p=11 To find : the elements of the…

Q: 4. Let L:R? - R³ be the linear transformation defined by x-y x+ y 2.x Let S be the natural basis for…

A: The given linear transformation is                 L:ℝ2→ℝ3 defined by Lxy=x-yx+y2x Also given that S…

Q: -AU (En F)

A: E∩F={3,9} So, A∪(E∩F)={3, 6, 9, 12, 15, 18}

Q: Vx.y" +x = 4, y(0) = 1, y'(0) = 11 %3D %3D

A:

Q: H.W. solve the following D.E. 1. (x + Vy? +1) dx - (y-) dy = 0 2. (e* + In y +) dx + + Inx+sin y) dy…

A:

Q: 4. Graph one complete cycle. Label everything! ! Fill in all the blanks. y = -1- 3csc( + Domain:…

A: The given function is y=-1-3cscπx2+3π4. To find: (i) Domain. (ii) Range (iii) Amplitude (iv) Period…

Q: Calculate t. [35 t+ 6 C 10 12 B O 25 O 26 O 30 O 28 O 27 O 29

A:

Q: . Let R be the relation on Z→ Z such that ((a,b),(c,d)) eR = a+d =b+c. Show that R is an equivalence…

A: An equivalency relation on a set is a reflexive, symmetric, and transitive relationship for…

Q: C. Solve as indicated. 1. How many terms are there in an arithmetic sequence where a, = 12, a, = 60…

A: We have to find the number of terms in the arithmetic sequence where a1=12, an=60 and d=8

Q: S 23x26 ++ : x-16 dx X-4

A:

Q: The ratio of the major axis to the minor axis of the ellipse 9x2 + 4y2 – 24 y – 72x – 144 = 0 is O…

A:

Q: 3. Show whether the following expressions are equal or not. Use tables or identities. x + (y z) = (x…

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Q: Please provide the solution to part (ii) for this question.

A: An expression for the angle FBC in terms of h is determined as shown below.

Q: The bus is late or my watch is fast.

A: Solution

Q: ди (х,у) — у. ди(ху) — и (х, у) с) х. əx ду

A: c) The given Partial Differential Equation is…

Q: (i) Sketch an odd periodic function of period 8. ƒ(L) = 4 – L, 0<L<4 (ii) Find the Fourier Sine…

A: Fourier series of the function

Q: Let A be a n × n matrix with real entries and let A1 = a + bi (where a and b are real and b# 0) be…

A:

Q: 2. Solve the following system of linear equation 2x +y – 2z = 1 3x + 2y – 6z = 2 x + 5y + 5z = 3 6x…

A: Let us solve the given system using Gauss elimination and LU decomposition method in the next step.

Q: y"+y = S(t-28) Cast, y10)= o, y'l0) =1 ノ Taking loplace transfoom on bath sides; L[ glty] =L[S(t-…

A:

Q: V25x² – 4 dx 8.

A:

Q: the ratio of the major axis to the minor axis of ellipse 9x^2+4y^2-24y-72x-144=0 is

A:

Q: Which triple integral in cylindrical coordinates gives the volume of the solid bounded below by the…

A: Solution:-

Q: A. List the elements of each set. 1. Set of all integers greater than 2 but lesser than 12. 2. Set…

A: Set Roster Notation: Roster notation of a set is a simple mathematical representation of the set in…

Q: Vector A = 6i + 2j - 3k Find the

A: Given: Vector A=6i+2j-3k  To find: Scalar component of A perpendicular to the x-axis.

Q: 2. In a certain university 2,191 students are enrolled in its College of Arts and Sciences. 980 are…

A: Let U be the set of all students in that university . M be the set of all male student and F be the…

Q: 5. Three apples and two pears cost 78 cents. But two apples and three pears cost 82 cents. What is…

A: Let the cost one apple and one pear is x ,y respectively. Then the cost of  three apples and two…

Q: The engineering department of a car manufacturer claims that the fuel consumption rate of a new…

A: For unknown population standard deviation, we use t- test. Formula for t - test statistics is as…

Q: Given the ellipse with equation 2x²+y?=1. Find a Maclaurin series that allows you to determine the…

A:

Q: find the general solution (solution set) of any LINEAR DIOPHANTINE EQUATION of the form ax + by = c.…

A: Take the linear Diophantine Equations 5x + 3y = 4  ,x , y ∈ Z

Q: Let L:R -R be the linear transformation defined by Find a basis for ker L.

A:

Q: 4. -5, -3-2, . 18th term 5. 16, 11, 6, ., 10th term

A: Part (4) We have -5, -312, -2, .... Subpart (a) Common difference is any term minus the previous…

Q: ( 2sinx sin(2x) dx

A: Given,        ∫2sin2xsin(2x)dx

Q: An ellipse has semi-major axis of 4 and its semi-minor axis is 3. The distance from the center of…

A: To find the distance from the centre of the ellipse to the directrix is

Q: How may sets of intersecting chords are there in the figure? [6 1 12 14 73° 4 1

A: Q.6 has answer 3

Q: Part 2. Use the integration techniques to solve for the antl-denV 1. 3p? tan p dp Integration by…

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Q: Mark has pairs of pants in three different colors, blue, black, and brown. He has 5 colored shirts:…

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Q: A. Perform the indicated operations on sets. 1. AUB 2. AnD 3. AUCUD

A: Given data:A={3,6,9,12,15,18}B={4,8,12,16}C={3,6,9,12}D={1,2,3}E={3,9}F={1,2,3,4,5,6,7,8,9,10}

Q: Continuous

A: We have to find what is continuous independence.

Q: Find a formula for the nth term of the sequence. 1, - 16, 81, - 256, 625, ... Determine the…

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Q: Solve the differential equation below over the interval from x = 0 to 1 using a step size of 0.2…

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Q: 3. The figure below shows twelve toothpicks arranged to form three squares. How can you form five…

A: Given:   the figure shows (in question) twelve toothpicks arranged to form three squares.

Q: Evaluate the given line integral. | (y, -x)-dR, where C consists of 4y = x² from (–2, 1) to (2, 1)…

A: Here we can use Green's theorem to find the value of the integral. Green's theorem states that if C…

Q: Next question Sketch the region of integration and evaluate the integral. xy dx dy Sketch the region…

A: We have to solve the given problem.

Q: 3. The general form of a linear, homogeneous, second-order equation with constant coefficients is…

A: Solution :-

Q: 1. The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

A: Let x be a first number.  Then, the other number is = (x + 9) Given, the sum of two numbers is = 25…

Q: 1. F(s) = 16/[s(s²+4)] 2. F(s) = (8s + 11)/[(s-4)(s²+9)]

A: We have to solve by inverse Laplace transform.

Q: -4 2 Given: A = 2 -7 4 has eigenvalues -3 and – 12. [-2 4 -7 a) Explain why we know that A is…

A: Given the matrix A=-42-22-74-24-7 has eigenvalues -3 and -12. (b) We will find an orthogonal matrix…