(a) Find all prime numbers p e N for which the equation z 43p +4 has solutions z EZ %3D

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A: 8)

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A: If x, y, z are related with the equation  fx,y,z=0then ∂z∂x=-∂f∂x∂f∂zand ∂z∂x=-∂f∂y∂f∂z

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A: Given:                     r = 7sinθ

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A: Let us start solving the problem step by step

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A: Making use of Tally method.

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Q: 8. {b € Z+ | -4 3 and d < 5}

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Q: VI. Use Lagrange Multipliers to solve the following: Maximize f(r, y, z) = 4x + 2y + z subject to 2…

A: Given function is  fx,y,z=4x+2y+z subject to  x2+y+z2=1⇒gx,y,z=x2+y+z2-1

Q: b) The following proposed proof contains two mistakes. Explain the mistakes. Result Let A and B be…

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Q: By Variation of Parameters 1) xy' + (1 – x)y = xe* 2)(x²

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Q: (c) Find the natural domain in R of the function f (x) = V4 – x + Vx – 3 Express your answer as an…

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Q: Y r = 4 sin 0 r = 1+ sin 0 B 2. Consider the polar curves (see figure above) r = 1+ sin 0 and r = 4…

A: Using the given picture. A and B lies in first and third quadrant so the angle lies between 0 and π

Q: Find the curvature of the curve 7 (t) = (4t, – 3t, – t) at the point t = 2. Give your answer to 2…

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Q: (i) X= “ABCDBCDC” and Y=” BCDCD” (ii) X= “POLYNOMIAL” and Y= “ EXPONENTIAL”

A: This is a problem of counting and finite math.

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A:

Q: 2х + бу 3D 16 Solve —3х — 9у %3D — 24 by Gauss-Jordan method а. (5, 1) b. (9t – 24, t) с. (16— 6t,…

A:

Q: For f(x) = x Apply the bisection method and calculate b2 (right endpoint after 2 iterations) 2 and…

A: Introduction: The intermediate value theorem is a continuous function theorem. In mathematics, the…

Q: az and dy dz IV. Suppose z is a function of a and y, and tan Vy? + 2 6y Solve for

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Q: 1. Let V = C[-n/2, 7/2] equipped with standard inner product. Show that (sin nr} U {cos mr}1 forms…

A: We will use the basic knowledge of orthogonal sets and vector spaces to answer this question. Basics…

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A: Solution :-

Q: 3 6. Work Problem 3 (- - ): V1 0 , v2 = 0 |2 vectors from 2 R³. (a) [ independent (b) . {U1, U2, V3…

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Q: Given the quadric surface z = * + draw level curves (contour lines) for the heights c = 0,5, 10, 15,…

A: Given surface z =x24+y22 To draw , level curves for c = 0, 5, 10, 15, 20

Q: b) Find the minimum number of terms of the series that we need to add in order to get Jerror| <…

A: Introduction: When the sign in an infinite series changes in alternative manner, the series is…

Q: -2 Find C2, where matrix C = [3/2 c. Lis 22! d. Lio 21 101 а. 15 l10 22] 3 b.;

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Q: Find a codomain B such that ƒ: A → B, ƒ(x) = e²´ is surjective. Show that g: B → A, g(x) = Vln x is…

A: As you asked only subpart (C) and (D) So, I answered here only subpart (C) and (D).

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Q: We consider the linear transformation T : R3 ------ R 3 T(x,y,z) = ( x+2y-z, -x+y+2z, 3z) 1. Give…

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A: Newton's Divided difference Method :- putting the value of Id in given table then  Current I at…

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Q: Solve each nonhomogeneous 2 3 1. 3 2

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Q: Consider the function g defined by g(r, y) = cos (Tx V) + COS log3(r – y) Do as indicated. 1.…

A: Instantaneous rate of change of a function g in the direction of the vector v is given by ∇g.u where…

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A: The area of a rectangle is calculated by multiplying its length by its width.

Q: 4 The integral " L* 1 dzdodr can be used to find the volume of a cylinder. Select one: True False

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Q: 505. Two tangent lines at the endpoints of a given arc containing 120° are drawn, and a circle is…

A: Solution :-

Q: 5) f(t) = f(t) = e¯2t/1+ sin2t

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Q: Given the tree below, find the following  a) Which vertex is the root? b) Which vertices are…

A: Here we use basic defnitions of tree

Q: Solve the system of differential equations x' = 16x + 36y y' = – 6x – 14y

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Q: The equation p =- in spherical coordinates 5 represents sphere.

A: This is a problem of spherical coordinate system, vector calculus.

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Q: x - 2 and ao = 0, bo For f(x) Apply the bisection method and calculate bz (right endpoint after 2…

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Q: Use the table below to find the percentage of data items in a normal distribution that lie between z…

A: To find the percentage of data items between two z - score of normally distributed data we just take…

Q: Determine the percentage of data values that lie between the upper and lower quartiles .

A: In a box-plot the left end line of box denote lower quartile, the right end line of box denote upper…