QUESTION 4 Calculate the area between y = 7 - x² and x-axis from x = -1 to x=2 as shown in Figure 1. (5 marks) y-7-x² Figure 1

Q: Classify the following quadratic forms: (a) 2x² + y² +22² - 2xy - 2yz (b) 3x² + 7y² +22² - 4xy - 4xz…

A: As per our guidelines we are supposed to answer only first question. Kindly repost other parts in…

Q: A. Sequences 1. Given that a2 = 6 and a€ = 96 are terms of a geometric sequence, find a4. 2. Given…

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Q: If 4 peaches cost $1.10 what will 6 peaches cost

A: Given, 4 peaches cost = $ 1.10 1 peache cost = $ 1.10/4                            = $ 0.275 Now, 6…

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Q: QUESTION 1 It is given that the radius of the semicircle increases at the rate of 0.5 cms¹ when…

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Q: show that V(x, y) = x 'f (2x+y) is the general Solution of X dv 2x dv ду = V ax

A: A partial differential equation is an equation containing more than one independent variable, one…

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Q: Q2/ For the given function x² + y² = 4,find a) Domain and range for the function. b) Graph of the…

A: Given the function x²+y²=2² (a) Here the function is the equation of the circle with radius 2 and…

Q: 2 m Find the angle theta. a = 5. b = 3. im N 1m D

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Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: As per the policy we are allowed to answer only one question at a time. So, I am answering the first…

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Q: 5s² + 25-4 (5+1) (S+2) (S+ 3) Taking inverse Laplace transform

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Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

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Q: 5. If Evaluate the following. (a) F' (9) (b) F (0), by interpreting F (0) as an area F(x) = √ √ 25 -…

A: Given: Fx=∫x525-t2dt

Q: Consider the following Gauss-Jordan reduction: 10 0 100 56 70 56 70 1 00 0 56 7 0 →> 00 68-69 010 =…

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Q: x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (a) f(0) is a local max and f(2) a local…

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Q: Find the eigenvalues and corresponding eigenvectors for the matrix 8 -8 -2 A 4 -3 -2 3-4 1 Write…

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Q: Determine the values of r for which the given differential equation has solutions of the form y =…

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Q: Determine the values of r for which the given differential equation has solutions of the form y = t'…

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Q: Consider the following two player bi-matrix game 19 6 19 1 -10 21 A = B = 0 7 12 6 14 16 2 -9 a)…

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Q: Solve the following differential equations, giving y in terms of x. dy (iii) cotx + 2y = sin 2x. dx

A: Let us consider a differential equation of the form dydx+Py=Q where P and Q are function of x  To…

Q: The polar curve r (0) = 1 - 2 cos(0) is graphed for 0 ≤ 0 ≤ T. Let R be the region in the third…

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Q: I. Solve the following Linear Systems of Equations by Gaussian Elimination: 1.) 6x + 2y4z = 15 -3x -…

A: Given system is 6x+2y-4z=15-3x-4y+2z=-64x-6y+3z=8 We can write it in matrix form…

Q: 3 By direct partial integration, Solve the following PDES & 82u axdy = cos x cosy, u(x,#) = x…

A: Solution :

Q: A. Sequences 1. Given that a2 = 6 and a6 = 96 are terms of a geometric sequence, find a4. 2. Given…

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Q: 10 [ Σ 15m3 n=m =

A: Given summation is ∑m=11015m3 we can write it as 15∑m=110m3         (1)

Q: 20 j ΣΣ (2k + 3) = j=5 k=0 = 2n+3 Σ (n + 5k)3 k=0 first step 2nd step final answer first step and

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Q: The behaviour of an unforced mechanical system is governed by the differential equation 5 2 -1 0…

A: Problem is solved using concept of matrix eigenvalue and eigenvector.

Q: Let b₁ 2 = sin−¹ (²) and c, = sin-¹ („²7) for all n € N such that n ≥ 2 +00 Σ(1+bn) n=2 Σ(bn-Cn) n=2…

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Q: II. Solve the non-linear equation: 1.) x2 - xy + 2y2 = 16 x - y = 2

A: Since x - y = 2 =&gt; x= 2+ y Therefore  x^2 -xy + 2y^2 =16 becomes (2+y)^2 -(2+y)y + 2y^2 =16 =&gt;…

Q: eigenvalues and eigenvectors a) Solve the following differential equations: x₁ = y1+3y2 y₂ = 4y1+5y2…

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Q: 5 Determinants Calculate the determinant of the matrices 0 1 0 0 0 a 0 0 1220 2403 0020 0003 M = , N…

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Q: Find the volume of the region bounded above by the sphere x² + y² + z² = 2 and below by the parabo-…

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Q: what is the vertical intercept of (1,750) and (2,562.5)

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Q: (E-₂) = given the linear transformation T: R³ → R² where T 7 (EFD)-6) and + (ED-C¹₂) a. If it is…

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Q: (f) V = {x € R: In converges as noo}, W = R, T(x) = limn → In, I EV; (g) V =R%, W = R, T(x) = -1n,…

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Q: By using the e- & definition, show that lim 2² + 1/{

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Q: QUESTION 2 The height, h, of a cylinder is two times its radius, r. If the radius of the cylinder is…

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Q: 10 Consider A = {z € C : |2|< 1}. The complex line integral Jonate=2) dz equals: (A) 0 (B)-ni+e²/2…

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Q: Evaluate the double integral: y С.Га y¹/3 x7 +1 (Hint: Change the order of integration to dy dr.) dx…

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Q: The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the…

A: Since

Q: Evaluate the double integral: Y [CZ (Hint: Change the order of integration to dy dx.) dx dy. y¹/3 x7…

A: We have to evaluate the double integral by changing the order of integration. ∫08∫y132 yx7+1 dx dy…

Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: To choose correct option form given question.

Q: ind the Wronskian of: 18x - 6 18x + 6 6x - 18 6x + 18 f₁ = x² - 6x f₂ = x² + 6x f3=x²-3

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Q: Q₂/(a) Let X=(1, 4, 5,7, 8, 9) and o= {(1,4),(4,7, 8}}, show that whether o is: (1) a subbase for a…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: In each part, solve the linear system, if possible, and use the result to determine whether the…

A: We have to solve the linear system and use the result to determine whether the lines represented by…

Q: 2. Use the equation 2 3 X1 0 +2 -3 + x3 2 + x4 -9 -7 3 0 2 for the following problems. (a) Write a…

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Q: Q.2 Check whether the following system given by its characteristic equation is stable or not and…

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