Take p and q are primes and p=3mod4 and q=3mod4. Take n=pq such that an integer z has a square root d mod n such that d^2=z modn. Explain why z also has a squar root mod p and mod q.

Q: lim 8-x3 x→2 (x-2)

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Q: Solve the differential equation (r² + 1)y – 2ry – 2x = 0 using the method of exact equations;

A: Differential equations

Q: 2x – x3 - 1. Evaluate dx. J (x – 1)²(x² + 1) - 2. Use the previous item to determine if the improper...

A: We have to solve integration

Q: 2 1 2 A = = | 3 -2 4 -3 -5]

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Q: 5 What is a. lim,-3 f(x) b. lim,-2 f(x) c. lim,0 f(x) d. lim,2+ f(x) e. lim,2 f(x)

A: To find the given limit values for the function using the give graph.

Q: functioN fo- x^-2X- 3 X+3 use second derivactive to idenfity intervals here fais cencave up L use se...

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Q: 17. Find the volume of the solid obtained by revolving the region bounded by the graphs of y = tan(x...

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Q: Find the Taylor series centered at c = -1. 7 f(x): %D Зх — 2

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Q: tan e de (1+ In cos ele

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Q: Determine whether g(x) is continuous on the following intervals. 1. (-5, -3) g(x) 2. (-3, -1) 3. (1,...

A: Given :   g(x) is a function that is :

Q: b) What could be the degree of f(x)? -3 2. -1- c) What is the sign of the leading coefficient? -4 -3...

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Q: 20. The cost of a certain piece of machinery is $700 and its value is depreciating with time accordi...

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Q: H.W: 1. find the derivative of the function f(x, y, z) = xy+ yz+ zx ,at the point P,(1,-1,2) in the ...

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Q: 2. Find an equation of the line that is tangent to f(x) = x³ and parallel to the line y = 3x + 1 (Hi...

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Q: Let

A: We will find the partial derivative with respect to x. 

Q: V1+x2 dx 3. J 3.s

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Q: For a given quadratic function f(x) = x- 42x + 98, %3D 1 Answer : (Choose the answer in the boxes) h...

A: Do the simplification and then compare with the standard form of equation and answer each part. 

Q: 1, 2, 3> and B = , P = (9, 8, 7) s the angle between A and B? (I should not have to specify this, bu...

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Q: The sin*3udu is equal to 3 А. — и + 1 - sinбu 12 1 -sinбu + 12 1 -sinбu + 12 1 -sin12u + C 96 1 sin1...

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Q: dy - (1 +x)y xy %3D dx

A: You have asked multiple questions and not mentioned  which question answer you need . According to b...

Q: 2. SOLVE THE GIVEN SYSTEM OF LINEAR EQUATIONS BY GAUSS-JORDAN METHOD. 3a + 4b + 3c + 5d = 23 2a + 3b...

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Q: Determine whether the series converges. 1 k=I V2k – 1 The series converges. The series diverges.

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Q: In constructing an open rectangular box from 588 ft of material, what dimensions will result in a bo...

A: Given problem:- In constructing an open rectangular box from 588 ft² of material, what dimensions wi...

Q: 5. f(t) = = cos 2t sinh 2t

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Q: 2tan4xdx 2 - tan~4x

A: Given problem:-

Q: x+1, (x< 3 Given f (x) = 2 x=1 %3D

A: Find your answer below 

Q: A company that manufactures bicycles has a fixed cost of $100,000. It costs $100 to produce each bic...

A: We have to find total cost of function and interpret C(90).

Q: 1 dx (V[1 - (In(x))?) X

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Q: 16. What is the derivative of f (x) = e8x+3? %3D a. f'(x) = e8 b. f'(x) = 3e8x c. f'(x) = 8e d. f'(x...

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Q: Find the volume of the solid with the base is the region enclosed by the parabola y = 1– x² and the ...

A: Here, the cross-sections to the x-axis are square. So, the side of the square is 1-x2. And, the area...

Q: Suppose Ryan borrows $9000 at an interest rate of 3% compounded each year. Assume that no payments a...

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Q: lim -Vx + e* + sin(x)cos(x) 1+ In (x)

A: limx→3-x5+ex1+ln(x)+sin(x)cos(x)=-35+e31+ln(3)+sin(3)cos(3)

Q: (=²+ 16) +c 483 V²+ 16 da. Vr? – 16 dz. - 74

A: ∫f(x)dx=F(x)+Cthenf(x)=F'(x)

Q: 4. Te- 105 has a half life of 203.9 hours. If there are 1054 g of Te - 105 initially, how long will ...

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Q: Expand the function in a power series E a„x" with center c = 0. Find a,x". 7+6x n=0 (Express numbers...

A: Radius of convergence of the power series ∑n=0∞anxn is given by, R=limn→∞anan+1 The series ∑n=0∞1np ...

Q: Given the graph below, evaluate the following limits: = b Retrieved from:basiccalc_initial_release_1...

A: Find your answer below 

Q: Find the value of x that satisfies the following equation (2x – 5yi) + (y + xi) = 8-7i В. 4 А. 2 С. ...

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Q: Question 3: Evaluate the following limits, if they exist, by using the graph -5 -4 -3 -2 -1 3 -1 -2 ...

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Q: X+2

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Q: Consider the following functions. f(x) = x and g(x) = x² – 10 %3D | Step 3 of 4: Find (fg)(-2). Answ...

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Q: Determine if -1 CSC 1 if 0 1 1 is continuous or not at r =; and 1. If it is discontinuous, identify ...

A: Given is the question of Continuity.

Q: Solve the systems of equation: Equation 1: x + 2y + 3zi = 20 + 5i; Equation 2: 5x - 3yi + 12z(1-2i) ...

A: Given x+2y+3zi=20+5i Equation 1 5x-3yi+12z(1-2i)=-50-180i Equation 2 x+yi+2z=20-10i Equation 3

Q: (x² + 1)y' + 2.xy + 2x = 0

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Q: children is based on the ratio of the child's weight to that of an average adult. The average adult ...

A: We will find how much a child should take for his medication. 

Q: need

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Q: 6, Solve the IVP 3w" -u'+ 2u0. u(0) = 2, u'(0)-0

A: The given equation is; 3u"-u'+2u=0, u(0)=2,u'(0)=0

Q: Let A = and B = , P = (9, 8, 7) b. find an equation for the plane containing A and B, passing throu...

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Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) =x +xy +y - 9x + 1 o...

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Q: Consider the following functions. f(-3) = 14 and g(-3) = –11 Step 1 of 4: Find (f + g)(-3).

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Q: S. xdx (x²+2)3 A 2(x+1) 4(x²+1)2 B +C 2(x+2) 2(x²+2) 2 +C 4(x²+2) 2(x²+2) ? D 2(x+2) 2(x+2)?

A: Substitute, x2 + 2 = t.