Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y® + 1, 1

Q: Solve using methods from differential equations A state has a current deer population of 120,000. It...

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Q: Find the matrix A of the linear transformation from R2 to R' given by 9 -8 (:) X1 T X1 + -5 X2. -5

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Q: a) Find C and k that show 8x? + 5x is O(x²). Show your algebra reasons. b) Use proof by contradictio...

A: Here given as  Tx=8x2+5x Use the definition of big-O notation Let fx and kx two real-valued function...

Q: Determine the coefficient of x65 in the full expansion of (x – 2)100. (You need not а. evaluate larg...

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Q: Let F, denote the nth Fibonacci number (F1 = F2 = 1, Fn+2 Fn+1 + Fn for n > 1). Use %3D induction to...

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Q: 6 (b). Let 0 < f(x) < cos x and 0 < g(x) < sin x for x E I. Show that there is ro E I such that f(ro...

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Q: The height of a ball dropped from the roof of a building can be found by using the model h(t) = −16t...

A: Given equation for height is ht =-16t2 +400 Here, t denotes time (in seconds) and h denotes height ...

Q: Finding the second derivative of the given vector function r(t) = 3t 4 1- 31 2 + 4t k.

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Q: – 1 (f •g)- = g-1 •f-17

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Q: Find the domain and range of the relation. Use interval notation where appropriate. Express numbers ...

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Q: Question 2 Let Di be the solid in space that lies in the first octant x, y, z 2 0, and be- tween the...

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Q: Pls do part b pls

A: Part (b)

Q: 6. Let a be a real number. Consider the series an = cos(n7); 2n +1 An, where n=0 (a) Is it possible ...

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Q: Graph A polynamyal of even clegree wbose leading 0oefficient is negative, ith 4 real zeos, an 'absol...

A: We will use basic concept of polynomials here Even degree means graph is like parabola

Q: Direction: Let y-fpx). Note any pattern and use this to determine the derivative of the other functi...

A: To solve this problem the main things is observed  the  pattern.  The complete solution of the given...

Q: rotating the given region about the specified line. yA 19-30 Refer to the figure and find the volume...

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Q: In R' you are given the vectors . а — (-21, -6, —3), and • b = (7, –23, – 15), and If q = (-147, 108...

A: Solution:-

Q: Given Pauli matrices X,Y, Z ; show that X2 = Y2 = Z² = 1 (a) by using the matrix representation (b) ...

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Q: Let A = {1,2,3,4, 5, 6} and let R be an equivalence relation on A. Suppose that 1R2, 3R5 and 6R3. Al...

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Q: 4. Assume y(x) = eaªcosBx is one of the solutions of the DE y(3) – 3y" + 7y' – 5y = 0. - - Then a + ...

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Q: How many times do you to multiply 4 by itself to obtain 64

A: We have to find the number of times multiply 4 by itself to obtain 64. Since, 64=4×4×4 Hence, if we ...

Q: (a) If z = w-2z, show, without breaking into real and imaginary parts, that 3z = 2w-w. (Hint: take c...

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Q: Show that the following SL problem has a negative eigenvalue y"(x) + Ay(x) = 0, y'(0) = 0, y(1) – y'...

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Q: . Find the rank of the matrix : 3 2 11 3 4 3 -1 2 2 Find rank of matrix

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Q: Add the numbers HA36 and BE36 in base 36, expressing your answer in the same form, i.e., in base 36 ...

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Q: 6. Based on data from the U.S. Department of Agriculture, the average number of acres per farm x yea...

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Q: Consider the two points P(0,5, 5) and Q(1,2,8) and the vector -1 v = -3 -1 You are given that PQ = -...

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Q: olleges. Arts and Sclences, Engir ing, Business, ing Arts. rental statons to be appor among the five...

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Q: 1 The expression log ), where a>0, is equal to a

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Q: Calculate the 35th term for this arithmetic sequence: 5, 9, 13, 17,..

A: Given, the arithmetic sequence is              5, 9, 13, 17, . . .      

Q: The following matrix: Page 2 1 -2 4 -1 5 0 -2 4 -7 1 2 -8 A = 3 -6 12 -3 1 15 0 2 -4 -3 3 12 0 has r...

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Q: Calculate the 10th term for this arithmetic sequence: 4, 1, -2, -5, ..

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Q: Let z = 6. and y Find the vectori = 47 - 7j and its additive inverse.

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Q: Find the length of the curve The spiral r= 3e 2, 0 s es 2 v3

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Q: Find the eigenvalues and eigenvectors of Pauli- X and Pauli- Y operators. Show that their eigenvecto...

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Q: Find the solution of t y" + 11y' + 24y = 70 e-1 with y(0) = 7 and y' (0) = 6. y =

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Q: Calculate by the Power Series Method the value of y as general solution (term-by-term from n = 0 to ...

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Q: 4. Assume y(x) = e«x cosBx is one of the solutions of the DE y(3) – 3y" + 7y – 5y = 0. - - Then a + ...

A: The given differential equation is y(3)-3y''+7y'-5y=0 and also given that y(x)=eαxcosβx is one of th...

Q: The number of visitors P to a website in a given week over a 1-year period is given by P(t)= 122 + (...

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Q: 3) f = {(0, a), (1, d), (5, e), (9, c)} find the inverse of this function.

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Q: If u- i+ j+ k, v= 10 i +4j+6 k, y w= 8 i+9j+7 k, evaluate the dot triple product (u x v) - W. 86 -10...

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Q: Given the points A(-9,4, –1) and B(-39, –2,-31) find a parametric equation of the straight line thro...

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Q: . Use mathematical induction to show that 13 + 33 + 53 +· ·+(2n + 1)³ = (n + 1)²(2n² + 4n + 1) %3D w...

A: We have to find the given statement using induction.

Q: 2.x – y+ z (1) Let T : R³ → R² be a linear transformation defined by T -x + y + 4z {v1, 02, 03} with...

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Q: Question 6 8(x,z) = 2xz+3z-x X-Z Let f(x,z)= Z. 2z2–3 Blank 1: Find the total differential of f(x,z)...

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Q: 9. 1 1 1 6. 1 1 1 You are given that the eigenvalues of A = 1 are 1 6. 1 1 1 1 6. 9,5,5, 5, counting...

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Q: 5. Find the solution u(x, t) of uz = tu4, 0 0, which satisfies the boundary conditions uz (0, t) = ...

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Q: b. Define a relation SER XR by S ={ (x,y) E R × R |x – y € Z }. Prove that S is an equivalence relat...

A: By equivalence relation, we mean that the relation is reflexive, symmetric, and transitive.Here we h...

Q: 15 14 14k 15* k=1 The series diverges.

A: Questions from the series.

Q: Use the formula for the binomial series: (1 + x)" : 1+ mx + 2! m(m-1)2 m(m-1)(m-k+l) +... k! m(m-1)(...

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