(a) Consider the initial value problem dy y(0) = 1. dz Verify whether conditions for existence and uniqueness theorem are satisfied.

Q: Sixteen people on a baseball team show up for a game. A.) How many ways are there to choose 10…

A: First we will know that , what is Combination and Permutation. A Combination is Selection of items…

Q: At a local market place, Naomi had 510 dolls to sell. In the morning, Naomi sold 160 dolls. In the…

A: Seven Thousandths = 0.007   Total dolls Naomi had = 510 Total dolls sold = 160 + 117 +100…

Q: Set up the iterated double integral in polar coordinates that gives the volume of the solid enclosed…

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Q: A researcher is interested in studying the connection between the time spent using electronics and…

A: b.) a group of 500 respondents from the ages of 13-19 who live in the state of New York

Q: -21 Let I be the line given by the span of 5 in R³. Find a basis for the orthogonal 8 complement L…

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Q: Evaluate J by means of Simpon's rule using n = 2m = 10 and h = 0.05. Reminder that the integral…

A: Answer is = 0.7468

Q: Solve the integral [e³+4x sin 2x dx using complex numbers.

A: Integration using complex number

Q: The position of the sun at sunset, north or south of due west, depends on the latitude and the day…

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Q: 3. Find the surface area of the parallelepiped with adjacent edges u = (4, 7, -8), v = (-2, 5, 11),…

A: Solution :18

Q: S ii) Show the DE is not exact (2y²+3x) dx + 2xydy = 0

A: Solution :

Q: 43.Given that Tree A is bipartite, which of the following gives the grouping of the vertices of Tree…

A: Given that Tree A is bipartite, which of the following gives the grouping of the vertices of Tree A?

Q: VI. Given a region R enclosed by the curves: π.χ. y = 1 + sin y = 4- ) 4 As shown below. (x - 2)² ,…

A: This is the problem of the volume of rotation.

Q: olve the following differential equation y" + 3y' + 3y = et sint, y(0) = 0, y'(0) = 1

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Q: Referring to Figure 11, suppose that fr F-ds=4n, fo F.ds = 4T Use Green's Theorem to determine the…

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Q: 2.) - x= x=0 d+y=1 given a x(0) = -1, y(0)=1.

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Q: would you solve this?

A: Given,       f(x)=x2-x-20, and g(x)=x2-8x+15

Q: 10. y" + 3y + 2.25y = 9t³ + 64, y(0) = 1, y'(0) = 31.5

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Q: Express the vector x as a linear combination of the u's. -17 U₁ = 0, U₂ = 5, U3 = 6, X = -43 -14…

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Q: What is the y-coordinate of the centroid of the plane region bounded by * y = x^2 - 4 and y = 2x -…

A: We have to find the y-coordinate of the centroid of the plane region bounded by y = 2x - x2 and y =…

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2, y = 1, and…

A:

Q: The following table shows the distribution of household incomes in 2010 for a sample of 1,000…

A: We can solve this using given information

Q: 43.Given that Tree A is bipartite, which of the following gives the grouping of the vertices of Tree…

A:

Q: 11. Find the measure of the angle between u = (-2,-2, 1) and v= (-3, 4, 0) to the nearest tenth of a…

A: Q.11 asked and answered.

Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 J= exp(-x² exp(-x²)dx [ Note that…

A: Given, we can write it as: J=∫01e-x2dx we have to evaluate J by using Trapezoidal rule when n=20.…

Q: - [₁ Le Evaluate J = dx by means of (2) with n= 10.

A: Solution:-

Q: 35. Which of the following statements is/are true? I. II. The height of the root of a tree is equal…

A: This is a problem of Graph Theory.

Q: (1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A: Let x ,y be two real numbers. We have to prove that the product xy is non negative if and only if…

Q: 13 2 1 Given A = 2 13 3, find wwww 4 2 1] the lower triangular matrix. [3 0 0 a. 2-1/3 0 C. [4 −2/3…

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Q: 1 J = [ exp(-x²)dx Evaluate J by means of Simpson's rule with n = 2m = 10 and h = 0.1 Evaluate J by…

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Q: (a) Solve the differential equation 1 "+y' + y = 0.

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Q: f(t) = **t +93 4. The Laplace transform 5 s² +45 +6 can be expressed as L{e [qssin(961) + 97cos(* *…

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Q: 5. Which of the following statements is/are true? I. II. The height of the root of a tree is equal…

A: This is from Graph theory.

Q: 8. The identity element of negative integers (Z-) under the operation * defined as a*b = min(a,b) is…

A:

Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 1 = [ exp(-x²)dx Note that this…

A: When n=10

Q: Prove that the following statements are EQUIVALENT: For any sets A and B, a. ACB b. AnB = A C. AUB=B

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Q: Let x, y E Rn be given. (a) If ||x|| = ||y|| = 1 and x y = 1, show that x = y. (b) If ||x|| ≤ 1 and…

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Q: A particle moves in two dimensional space where i and į are unit vectors in the x and y directions…

A: given  r→=6t-4t2i^+2t j^ a) write down the particle's velocity vector in component form. ii) find…

Q: Evaluate the following [8(t+ 3)e¹dt 88

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Q: 3. Prove that if G is an open set dense in the metric space (S, d) then SG is nowhere dense in S.

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Q: (a) Determine whether the set of functions is linearly independent on the interval (-∞, ∞). f₁(x) =…

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Q: 1 2. Σn=10"+ 5n · (Comparison Test)

A: We will use comparison test for series.

Q: Consider the points A(2, -1, 3), B(7,0, 5) and C(0, 1, 7), and the line with symmetric equations…

A: We will use vector properties and equations of line and plane to solve all part  Note : I have…

Q: F(s) 8Bs - 7C (s + 3)(s - 4) (As − 1)

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Q: Find the inverse Laplace of Find the solution of the DE using Laplace Transform y" - 4y +4y=cos(t);…

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Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

A: Here we use basic shell method.

Q: Find the solution of the given initial value problem in explicit form. 75 π sin (2x) dx + cos (7y)…

A: The given initial value problem is                        sin2xdx+cos7ydy=0,  yπ2=π7 We have to find…

Q: f(x,y) = (x³ − x)(x² − 1). find fxy(x, ×

A: We have given that ,  fx , y = x3 - x y2 - 1 We need to find , Partial derivative fxy . We know that…

Q: y 8 7 6 4 3 -2 The diagram shows the shaded region bounded by the curves y = x² + 2, y = 4 - x, y =…

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Q: 1 1 = 5° 0² J exp(-x²) dx

A: Using trapezoid rule

Q: Find the inverse of the following matrix 2 3 0 1 4 6 ol

A: