Q3 Let A(1,0,-1), B(-1,2, 1), and C(1, 2, -2) are the three points in a 3D coordinates system. a) compute the cross product of the two vectors AB and AC b) Can we say that the obtained cross product is perpendicular to both vectors AB and AC? justify your answer and show your calculation.

Q: Sketch a graph of the function f(x) = 3 cos 6 5 4 3 2 1 -8п -7п -бп -5п -4п -3л -2л -π -1 -2 -3 -4…

A: This question is based on graphing a function from its principal function.

Q: Write the partial fraction decomposition of the following rational expression. 3x² - 8x + 20 X(X +…

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Q: Integrate (sinx + cos^2x)^3 dx

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Q: [3 -2 21 The matrix A=0 -2 1 one of the eigen vector is (solve) Lo 0 11 250 Option 4 O [3] -2 -31 2…

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Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: Question 10 Evaluate the following expressions. sin (tan-¹(√3)) cos (tan-¹(1))

A: By triangle property

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Q: OLA: Solve the following system by (method of inverse) 2x₁ + 3x₂ = 5 x₁2x₂ = -1

A: Given problem:- Solve the following system by (method of inverse) 2x1 + 3x2 = 5 x1 - 2x2 = - 1

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Q: Question [ a) [1 b)' 1. : Evaluate 6 1₂° ₁x + 2 ): If Show all your work. then find f(x). c) [ graph…

A: a)∫26 (x+2)x-2 dxLet    x-2 = z2      implies     dx =  2z dzx=2   ⇒ z =0x=6  ⇒ z= 2The integral…

Q: A. Using convolution to find L-¹ [(5+2)(5+4)]. B. Test the divergence of the following series 00 n

A: Note:- according to the company policy we can attempt only one question so please upload the next…

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Q: Convert the rectangular coordinates to polar form (√8,√8) (4,57) (√2,73) Option 4 O Option 1 (2,3)…

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Q: answer = Σ n=0

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Q: The distance from the point K(3, -2, 0) to the az- plane is Select one: O-2 O √13 O 0 02 O None of…

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Q: Let à = and b= . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

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Q: Find the radius of convergence for: 3 (n!) ³ (3n)! n=1 xn

A: Recall that the radius of convergence for a series ∑n=1∞anxn is R=limn→∞anan+1

Q: -S 3x²-6x+7 x3-x²-x+1 dx

A: Solution of given question is written in below steps.

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A: Given that graph of y=rtA.gt=sin3πrtg't=cos3πrt×3πr'tg'1=cos3πr1×3πr'1r'1=slope at…

Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

A: Use arc length

Q: The value of the definite integral 3 [² (3x² Jo 0 is (3x² - 2x + 4)dx

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Q: Evaluate the following integral. 22x² S= x4-61x² +900 Find the partial fraction decomposition of the…

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Q: Let à = (4, — 5, — 4) and 6 = (2, — 5, 0). Find a - b

A: Let a =< a1,a2, a3 > b = < b1, b2, b3>  Then,  a.b = a1b1 + a2b2 a3b3

Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

A: We can find the area of the bounded by the given curves.

Q: If b) [ f(x)dx = = n(x)) = 1 then find f(x). = + = 2 x ² + 6x -tan(x) - 4e + + 6x + C

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = xy² + 9, D = {(x, y) | x ≥…

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Q: The two vectors a = (-1,2,-4) and b = (2, -4,-8), are not parallel but are orthogonal. Select one: O…

A: Given vectors:- a=-1,2,-4 b=2,-4,-8

Q: Find the differential equation by eliminating the arbitrary constant/s. 1. y¹= x(2e + c) 2. y = Ae³x…

A: 1. y-1=x2ex+c Note:     Multiple questions are given, we are answer with only one question. If you…

Q: f'(x) = x²¹ - 2x² x¹2x² 2x−² + 1; f(1) = 5

A: Given that f'(x)=x-1-2x-2+1 -(i)Also given that f(1)=5.Our Aim is to calculate the antiderivative of…

Q: Find the area of a triangle PQR, where P = (6, 3, 5), Q = (0,4, -3), and R=(-6, -1, - 5)

A: As we know that; The expression for the area of the triangle PQR is: A=12PQ→×PR→   Given: P=6,-3,-5,…

Q: If 4x² - y² = 64, show that ds² = 1/2 (15x² (5x² - 16) dx².

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Q: Evaluate tan(2x + 5)dx 0.0190 0.9899 0.0976 -0.0190 0.0967 0.00190 0.0109 0.9998 -0.0976 -0.8999…

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Q: S cos 2x dx COSX

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Q: Find an equation of the plane. The plane through the point (6, −8, −8) and parallel to the plane…

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Q: Find a plane containing the point (-1,-7,-8) and the line of intersection of the plan 6x + 4y + 4z =…

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Q: Let f(x) = be a piecewise function. Evaluate So fo f(x)dx= 3x²+2, 2x - 3, if x < 2 if x ≥ 2

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Q: x² + y² = 7 X=7 O igular (solve) x² + y² = 49. - Option 1 O

A: Given that r=7  r2 =49 let x= 7 cos(theta) y=7 sin(theta)

Q: Express the equation in logarithmic form: (a) ex = 5 is equivalent to In A = B. Then A = and B = 3…

A: To express the equation in logarithmic form:a ex=5 is equivalent to ln A=B. Then A=?and B=?b e3=x is…

Q: Evaluate the expression under the given conditions. sin(20); sin(0) ==, in Quadrant II 0

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Q: Find all the values of x such that the given series would converge. (8x)" n11 n=1 The series is…

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A: NOTE: Refresh your page if you can't see any equations. . the given equation is take derivative

Q: an = arn+1 an arn-1 Option 4 The general term of geometric progression is an=arn a" = arn-1 Option 3

A: Topic = Series

Q: The table gives the values of a function obtained from an experiment.

A: As per our guidelines we are supposed to to only one question at a time. Kindly repost other…

Q: Determine the area of the shaded region. 70. 15 4+ 3+ 2- 1 이 12x - x2 2 becodelating onesyde, −12 +…

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Q: Consider a solid G, generated by rotating the region bounded by y = 2x² and y = 0 from would the…

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Q: Give a possible formula for the function below. Let A = (-1, 32) and B = (1, 8). Use the general…

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Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

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