030: Define nilpotent element. Are 1 and 3 nilpotent elements of Z11?

Q: swer no. 1 and

A: 1. Given,           A=R, (a*b)=a+b

Q: Given f(x) = |x| for x € [-n,1]| Show that cos(2n – 1)x |x| 2 \xl = -- - (2n – 1)2 n=1 2.

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Q: Q.12) The solution of y" + y' = 0 by using power series method , is! %3! a) y(x) = a, – a,(1-+ b)…

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Q: Сompute f dx, where f(x)=|x|.

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Q: Mark has pairs of pants in three different colors, blue, black, and brown. He has 5 colored shirts:…

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Q: How far trom the y-axis is the center of the curve 2x? + 2y? + 10x - 6y - 55 = 0? O 2.50 O 2.75 O…

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Q: Evaluate the guea linie integal- dR,wheru ConGiste the cuito x ty": the spper part g the ails x'ty*…

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Q: Use the Fuler methad's Solve the; g(0)-1 hこ8r

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Q: C. Write C if f is continuous on the given interval, otherwise, write N. Write your answer on the…

A: Note:- Some information about Intervals:- Open Interval:- An open interval does not include its…

Q: A random variable x that is distributed normally with a mean of 5 and a standard deviation of 2. 1.…

A: Normal distribution z=x-μσ where μ is mean of the random variable  σ is standard deviation of the…

Q: The eccentricity of an ellipse with the equation 16x? +9 y + 32 x – 128 = 0 is 0.53 0.66 0.82 0.93

A: We have to find the eccentricity of the ellipse  16x^2+9y^2+32x-128=0

Q: Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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Q: 3. Evaluate the integrals: I, - [sin'xdt and /2 = sin-xdx using the following methods: (a) Simpson's…

A: As per policy , we are allowed to answer one question at a time . So , I am answering the first…

Q: Determine if the following function is periodic. If it is periodic find the fundamental period, p.…

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Q: Find the g.c.d. in Z[i]  of 2 and 3+5i.

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Q: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 1 from…

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Q: Consider the function g defined by 1 g(r, y) = cos (7IV) + log3(r – y)" Do as indicated. 1.…

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Q: Find a, b and c so that the quadrature formula has the highest degree of precision f(x)dx af (1) +…

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Q: Calculate x in degrees. [22 8X +5° 3X + 8°

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Q: Given the angle equals n/6 where. Calculate the combined circumference of the two circles minus the…

A: Q.38 Given the two circles with radius of one circle r1=10 and the distance between their centers is…

Q: 4. lim f(x) = +∞, x-3 lim f(x) = -o x-3+

A: This is an application of calculus.

Q: Evaluate the given line integral. (y, -x) · dR, where C consists of the uppder part of 2² + y? = 1…

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Q: c) (-1)"xm 0.12) The interval and radius or convergence for power series m=0 h) (-00, +0), 1…

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Q: (a) Consider the differential equation -u"(x) = x in (0, 1), u(0) = u(1) = 0. (v) Taking a mesh with…

A: Given: The differential equation, -u''x=x in 0,1. The boundary conditions: u0=u1=0.   To compute:…

Q: Given the angle equals n/6 where. Calculate the combined circumference of the two circles minus the…

A: Given two circles C1 and C2 with centers at A and B Radius of circles C1 and C2 are r1 and r2 Given,…

Q: Evaluate, the ie idegal- dR, where ConGists of X- the upper part g the cite i'ty the curife * 1 from…

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Q: QUESTION 1 Which is the contrapositive of "If March comes in like a lion, it goes out like a lamb"?…

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Q: y QUESTION 4 В(4%;B 12) E C А(-5; —3) 4.1. Calculate the gradient of AB. 4.2. Determine the…

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Q: 7. (Refer to HW#5: Section 2.3 - Exercise 2 ) Consider the following second-order equation: 6 + 7y =…

A: As per our guidelines we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: b. Give examples square matrix, diagonal matrix and scalar matrix. c. Solve the following equation…

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Q: Based on tha sales data for the last 30 years the linear regression trend line equation is:…

A: Solution :  Given that  The linear regression trend line equation is  Ft = 93 + 24 t

Q: Solve [a – y cot ()) dæ + a cot () dy = 0 ; y (5) = 1

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Q: Find a, b and c so that the quadrature formula has the highest degree of precision f(x)dx = af (2) +…

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Q: Question 40 Calculate the arc length of the unshaded region. [40 ] 4 ft Po 80° D. O 54n/9 ft O 19.4…

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Q: 9. Jesse was riding her bicycle and ran over a nail. At this point, a stopwatch starts timing. The…

A: If height denoted by cosine function  ht= a cos bt +c +d  a is amplitude  2πb is period  c is phase…

Q: Find the volume of the solid obtained by rotating about the y-axis the regioN bounded by y= 2x- x…

A: The given curves are y=2x2-x3 and x-axis. To find: the volume of the rotated region bounded by the…

Q: Solve (xy + x/2 + y+ v2) dx + (x²y+ y – x² /2 – v2) dy = 0 - -

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Q: Find the general solution of the differential equation: (1+cos(I)y-(sin(x)y 2x y'+ sin(a) 1+co6(x),…

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Q: 1. Evaluate the given line integral, | (x – y, y) · dR, where C is the left part of x² + y? = 1 from…

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Q: 9. I= set of all positive even integers, (a*b) = (a-b)/2 10. J= set of all positive odd integers,…

A: If the set does not satisfy any condition then we will not check the next conditions...

Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos…

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Q: Let X be the vector space of all or Can we obtain the norm defined on from an inner product?

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Q: 3. Find the parametric equation of the line passing through the point (-1,0, 3) and in the direction…

A: Equation of the line passing through the point (-1,0,3) in the direction N(7,0,-2) is   ( x+1)/ 7 =…

Q: 2. Convert the following: radians to degrees 225° to radians

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Q: . Consider the autonomous first order equation dr = r*(1 – r²). dt Find all critical points, and…

A: Derivative of the function f(x) is the measure of how fast the function is changing with respect to…

Q: 4. Graph one complete cycle. Label everything! ! Fill in all the blanks. y = -1- 3csc( + Domain:…

A: The given function is y=-1-3cscπx2+3π4. To find: (i) Domain. (ii) Range (iii) Amplitude (iv) Period…

Q: 4. Determine the exact value of the following. tan? () – sin (;) cot (A

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Q: Q1 (a) Find the general solution to y" + 2y' + 2y = 0. (b) Write down a linear, homogenenous 2nd…

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Q: Romberg integration for approximating S, f(x) dx gives R21 = 2 and R22 2.55 then R1 %3D 0.35 2.15.

A: Introduction: Romberg's approximation is used in numerical analysis to approximate the definite…

Q: Let k an even natural number, k > 4. Solve in Z the equation: 11...121 = x². k-2 times

A: We show that the given equation has no solutions in Z by reducing modular arithmetic mod 11