1. Find the extreme value of the following function and check whether the extreme value is a maximum or a minimum. z = 3x – 5 y² – 225x + 70 y + 23 -

Q: 2. In each of the following cases: parametrize the curves; and determine whether the curves are orth...

A: (a) The two curves are given as : curve I : y = x2     .................(I) curve II :  x = y2    .....

Q: 3. f (t) e2t Cos 5t 3t3

A: Laplace transform formulas need to be known. They can be obtained from here: https://tutorial.math.l...

Q: 8. A plane intersects the center of a sphere that has a volume of 1436.76cm3. a. The cross section i...

A: 8. 1. Solution: Here the sphere is cut by plane from center. Here we may observe that the shape of ...

Q: 1. Evaluate the integral ab- a + b à) + a(b a)-2(à ab - bla dt in which a, b are the derivatives of ...

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Q: (AUBUC) (A UB)nC (A - B)n (A - C) (B – A) (C -Ā)UB

A: Solution:

Q: Let f = ao+ajx+…+a„x" be a polynomial. I can treat f as an element of R[x] by defining an+1,&n+2,......

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Q: 223+-5 -j Suppose z1 = 2+ j, 2 = 3- j2 and z3 = -+j Evaluate %3D 2-a+3-j

A: Substitute the given values of z1,  z2, z3 in the given expression and simplify. 2z2+z1-5-j2z1-z2+3-...

Q: Muir Manufacturing produces two popular grades of commercial carpeting among its many other products...

A: Let Muir need x rolls of Grade X and y rolls of Grade Y such that the proof is maximize. Then, we ca...

Q: n n Proposition 10. Let n and k be positive integers. Then k = n k k - 1 Special directions: Your pr...

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Q: The value of the integral sin() dy dz is

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Q: ADVANCE ENGINEERING MATHEMATICS: Answer the following with explanation What Mclaurin Series this fun...

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Q: y У — х. y' = 2+ sin

A: Given y' = yx + siny-xx    ---(1)

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied by the function f defined by f(x)...

A: Please see the attachment

Q: g(t)= 2e"u(t – 1) p(t) = 6[u(t – 2)– u(t –4)]

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Q: Drawing a Ticket from a Bag P(x) 2 1 5 1 2 3 4 5 Number on Ticket Probability

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Q: 7. Check if the following graphs G and H are isomorphic. G: H:

A: Given the graphs G and H below.

Q: I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 7. For any sets A, B, ...

A: Given that  for any sets A,B,D, if B⊆A then D-A⊆D-B We have to check that the above statement is tru...

Q: Proposition 6. Consider the function g : Z? → Z² defined by g(m, n) = (m – n, n – 2m). The function ...

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Q: Show illustration and define variables used. 1. A statue 10 feet high is standing on a base 13 feet ...

A: Given: Statue is standing on a base which is 13 feet high, and height of statue is 10 feet. Height o...

Q: If z = x2 + y?, x = e' cos(s) and y = e' sin(s), then %3D dz at (t, s) = (1,0) is as %3D

A: Given that z=x2+y2, x=etcoss and y=etsins First we have to find ∂z∂s.

Q: Determine whether each of the following statements is true. If true, prove it. If false, give a coun...

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Q: Solve xy' (2y - 1) = y (1 - x)

A: Solve xy' (2y - 1) = y (1 - x)

Q: 5. Divisibility Prove that if alb and bla, then a = b or a = -b.

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Q: Evaluate by changing to spherical coordinates: /2–x²-y² xydzdydx x²+y2

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Q: Σe0 = 1+z+ = 1+ x + -k=0 2! 3! 4! + +

A: This is a question oof Mclaurin series.

Q: Round 234 to the nearest ten and hundred.

A: The hundreds place, tens place and unit place of a number can be represented as:

Q: Find the extreme values ​​of f(x, y) = 2xy subject to the condition x + y = 2.

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Q: Let F be a commutative ring with identity and let f (x) E F[x] be a polynomial of degree 4. Which of...

A: Given: It is given that the function is with degree 4.

Q: Find the function f(x) = Ca whose graph is given. f(x) = (x, Y) = (-3, ) 40 %! 27 (x, y) (0, 5) y 10...

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Q: Proposition 5. Consider the function f : Z² → Z² defined by f(m, n) = (mn, m+n). The function f is n...

A: Remark: Let f be a function from a non-empty set A to another non-empty set B. Then f is Said to be ...

Q: Consider a dynamic system described by the following integro-differential equation 4x+3x+2x+5| x(t)d...

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Q: find the measure of <1 243°

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Q: Q.2 Find the vertex point and show in graph: y=2x-4x+4

A: The given equation is a quadratic equation and as we know  that every quadratic equation forms a par...

Q: The function is n+1 = 3 + 0.8 (x – 1) (x – 4) - -

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Q: Given the function below

A: Given,           f(x)=-162x3+8913

Q: I. Consider an = V4n² + 3n – 2n for n >1. 1. Determine if {an}-1 is convergent or divergent. 2. Is >...

A: Simplify the expression of an. Multiply and divide the given expression of an by 4n2+3n+2n to simpli...

Q: The plot above is created with the parametric equations ( ¤(t) = a cos(bt) y(t) = c sin(dt) %3D

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Q: Problem Solving 1. Find the values of x and y using Determinant Method and Gaussian Elimination 4х —...

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Q: 1. f(t) = -e-3t sin 4t + 3

A: L { sinat } = as2+ a2 , L { eat f (t) } = F ( s- a) where  F (s)  is Laplace transformation of f(t)L...

Q: (3 + 5y +7{ ) 2+y? 200 + y02 exists if lim r)(0.0)

A: This is a problem of multi variable calculus.

Q: Which of the fo A O Diagram O Diagram

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Q: The lines / and m have equations r 3i- 2j+ k+1(-i+2j + k) and r 4i + 4j +2k + u(ai+ bj- k) respectiv...

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Q: Let g be a decreasing continuous function on [0,1), assuming the values g(0) = 1 and g(1) = 0. Show ...

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Q: Proposition 8. Let m be any integer. If 5|(7m), then 5|m.

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Q: 5.identify the fixed points, cobweb the diagram, and assess whether the fixed point is an attractor ...

A: This is a dynamic system problem.  

Q: Question 6 i P Consider a room in the shape of a 4 m cube, 4 meters on each side. A bug at point P w...

A: We need  to find shortest distance between two diagonally opposite corners of the cube .(along the s...

Q: +o0 Σ)

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Q: Ron's Recycle Shop started when Ron bought a used paper-shredding machine. Business was good, so Ron...

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Q: A statue 10 feet high is standing on a base 13 feet high. If an observer's eye is 5 feet above the g...

A: This is the problem of application of differential calculus.

Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

A: