How many funcei ons F{,2,3,4is}→ {l,2,3} are ehere eien er FCI)=1, F(2) 2, f (3) =3? or

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: If T : R? → R² is a linear transformation such that 7 (1) - 5 34 6 30 T and T 21 then the standard…

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Q: Question 5 Find a 4x4 matrix A (NON-ZERO ENTRIES ONLY) with 3 eigenvectors coming from a single…

A: We want to find the required matrix.

Q: A number is drawn at random from the integers 20 to 40. Let A the event that the number is not less…

A: We have to solve the given problem.

Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 5 6 Y 4 9 10 10 8 O3

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Q: Suppose two cylindrical tubes with the same diameter intersect at right angles. If the diameter of…

A: To find the volume of the common part between two cylindrical tubes kept at 90° .

Q: Continue the two sequences of numbers below and find an equation to each of the sequences 1 2 3 4 5…

A: 1. In first. 1+1=2 2+3=5 5+4=9 9+5=14 14+6=20 20+7=27 Hence the eqution is  an=an-1+n

Q: L. RELATIONS Let C= D= {-3, -2, -1, 1, 2, 3} ar For all (x, y) E Cx D, (x, 1. a. Is 2 S 2? b. Is -1…

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Q: b) Given that z, = V3 +i and z, = -2- 3i . Find the modulus and argument of and %3D Hence, express…

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Q: Consider the solid bounded by the planes: z=x+y, z=30, x=0, y=0. Determine the volume of the solid.…

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Q: Find the Green function of L[x] = x" on [–1, 1].

A: As per the question we have to find the Green Function of the operator L , defined as : L[x(t)] =…

Q: Q3. Tangents are drawn from 0(0,0) to the circle x² + y² – 2x + 4y+ 1 = 0, touching the circle at L…

A: The standard form of the equation of circle is   x-h2+(y-k)2=r2   where (h,k) is center of circle…

Q: Q2/ Fit a second - order polynomial to the data in the following table: 5 1 4 2 7 Y 2 8 3 4 -1 8 4

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Q: What are the possible rational roots of the equation x + 6x2 11x + 6 = 0 A. -6, -3, -2, -1 C.+6, +3,…

A: Rational roots of polynomial  Let us consider a polynomial of the form…

Q: Q5) Find volume of body bounded by z = -y? from below and z = x? from above inside y = 0,y = x,x 1.

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Q: Question 2 [ region below x first octant. Evaluate the following triple Let E be the 2y + z= -1 in…

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Q: Let p be an odd prime. Suppose p5 mod 8. Show p-1 p? – 1 mod 2. 5

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Q: Use truth table to establish the truth table of following 1)A conditional statement is not logically…

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Q: Q1) Evaluate the integral Sdy dx using polar coordinate

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Q: Q1) Evaluate the integral S dy dx using polar coordinate

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Q: 1-4, apply the Jacobi method to the given system of linear equations, using the initial…

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Q: Q42. The value of p and q respectively when (p + q) V p is false is? (a) T, T (b) T, F (c) F, T- (d)…

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Q: 3. Prove F (Vr)(A→ B) → (Vx)A → (Vx)B. ->

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Q: √3. (2√27 + √12)

A: Given expression: 3·227+12

Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) d²y + 2y = 3 , y (0)…

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin 2 + 0) in…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y x2,y 4.

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Q: 1 2 3 4 5 6 Y 4 10 10 8 3

A: Here follow the python code.

Q: Q3) Evaluate triple integral , dz dy dx .

A: Given integral is ∫-22∫x24∫04-ydzdydx

Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: 1.7 1.8 1.9 2…

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Q: r1.5 (3-y dx dy using polar coordinate Q1) Evaluate the integral o

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = -2cos0 in second…

A: Solution

Q: |I+ sin? 0 2. Cos? 0 4 Sin 20 Sin?0 一t Cos 0 · 4 Sin 20 %3D Sin 20 Cos20 I tA sin 20 KIKY

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Q: dz + (y + z) dx dz surface of sphere

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Q: . Rolle's Theorem: Assume f has a derivative (finite or infinite) at each point of an open interval…

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Q: dy Find given x' +y =8.y. dx

A: Here we can use implicit differentiation for finding the value of dydx. For the purpose we need to…

Q: 1 (i) Find the unit vector having the same direction as B – 2A+÷C. (ii) Draw the vector you obtained…

A: We have given three vectors A, B and C .

Q: Give the VALUE only. No need to include the unit. Let s, =15r +10r +20 and s, = 5r + 40r , t 2 0, be…

A: Given positions functions are SA = 15t2 + 10t + 20SB = 5t2 + 40t

Q: 3. Compute the product M()M() as a 2 x 2 matrix. What kind of isometry is this product? If it is a…

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Q: For each problem, use a left-hand Riemann sum to approximate the integral based off of the values in…

A: We can solve this using formula of left Riemann sum

Q: What is the equation of the normal to the curve x^2 + y^2 = 25 at (4,3)? 5x+3y=0 3x-4y-D0 3x+4y=D0…

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Q: Q1) Evaluate the integral S dy dx using polar coordinate

A: We have convert the given problem into polar coordinates.

Q: c) By using De Moivre's theorem, find (3/5 – 3i) in the standard form.

A: To find complex no. in standard form using De Moivre's theorem .

Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) + 2y 3 ,y(0) = 0,…

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Q: Solve the equation Ax = b by using the LU factorization given for A. 4 - 4 4 1 0 0 4 - 4 4 - 4 A = -…

A: We want to find value of x and y

Q: Solve the equation Ax = b by using the LU factorization given for A. 4 - 4 4 1 0 0 4 - 4 4 - 4 A = -…

A: Let us consider the system of equation in matrix form Ax=b To solve the system of equation using LU…

Q: x² + y² + 2z² – 2x + 8y – 12z + 35 = 0

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Q: A chance of 75 out of 100 0.5 0.01 0.1 0.75 0.25 O 1

A: To find: A chance of 75 out of 100

Q: If uxv=uxw, u 0 then Ou=v+ kw None of the choices O v= w+ ku O w=u+ kv

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Q: Find plane area inside the polar functionr 2 and outside polar function r 2 sin +0) in second…

A: Area using polar coordinates is given by  A=∫∫A r dr dθwhere x=r cos θy=r sin θ