The number of units in Z31[x] is None O 22 O 28 О зо

Q: Find n, where (x²+ ax+)² o(x"). Hint: expand (x*+ax+J

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Q: Calculate M, for f(x) = 6 · In(æ³) over [1, 2]. M6 ||

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Q: 7. Remwrite the..either.five.exated.nt.agrmls. 1-X FCX ng , Z)dydzdx ZA z= 1-x2 ...... y=1-メ

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Q: Evaluate fc 713 where C : |z| = 2. Ans. fc z+1)3 Ti ( – 4). 1 z² (z+1)³

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Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

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Q: Let 21 = 2+ j3 and z 4 j5. Evaluate

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Q: An automobile service facility specializing in engine tune-ups knows that 50% of all tune-ups are…

A: Given: 50% of all tune-ups are done on four-cylinder automobiles. 20% on six-cylinder automobiles…

Q: The value(s) of x that satisfy In(x² + 1) – 2 In(x) = In(16) – In(8) are/is

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Q: Find z-transfrm for (n-1) X(n) u(n-1) x (n) 5nucn) - 2 n (o.3) uci) 2)

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Q: Ive for æ if In(x? – 1) = 0.

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Q: Express In V16 in terms of In 2 and/or In In 16 =[ (Type an exact answer.)

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Q: 4. Find the critical numbercs) for gx) =IRCX+1) t, en cuaracterize ealh, one as 1ocal min, or…

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Q: Prove that no (nº.2)

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Q: 6. Evaluate In (x - In (r-...))dr in terms of some new variable t (do not simplify).

A: Given :- ∫lnx-lnx-...dx To find the given integral in terms of some new variables t

Q: Find the product and addition of the approximate numbers x, = 32.452 and x, = 24.3595 all of whose…

A: x1=32.452 and x2=24.3595 To Find: a) Product and addition of the approximate numbers. b) Relative…

Q: et z = 6ex²y³ find O 12xy³ex²y³ O 18x²y²ex²y³ O 18xy³x²y³ O 12x²y²ex²²³ дz ax

A: Given, z=6ex2y3

Q: Verify that v2+ V5 is algebraic over Q.

A: Algebraic number :- An algebraic number is a number that is a root of a non-zero polynomial in one…

Q: (b) Show that o = 2[Rx(0) - Rxx(0)] XX

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Q: Q3: Prove that (9":n e Z) (3":ne Z) but (9":n E Z) (3":n E Z).

A: We have to prove that 9n:n∈ℤ⊆3n:n∈ℤ but 9n:n∈ℤ≠3n:n∈ℤ

Q: 1. • If r + 1| < o, prove that |r³ + 1| < 0.331.

A: Here we use the fact  | x |&lt; a implies  -a&lt; x &lt; a .

Q: 00 8tan-in Zn=1 n3D1 1+n2

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Q: Find the interval of En=0 2" (z – 3)" O (2.5, 3.5) O (2, 3) ( (3.5, 0) O(2.5, 0)

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Q: is equal to Vy V27x O True O False

A: 3x2y327x

Q: It is always true that SŠ S Lº 1 dzdydx = 30. O True O False

A: Hi there, At a time we can answer only one question and you was not specify the exact one. So, I…

Q: 81/ show that *if ve(Xジーズ) oif v=(

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Q: 18. Find Itm,..(xe -x) O 2 O O O

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Q: What is the general rule to evaluate I N,where N is any positive

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Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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Q: P-value = 0.072, a = 0.05 O reject Ho O do not reject Ho P-value = 0.005, a = 0.001 O reject Ho O do…

A: We need to determine the decision based on the given p-values and significance level.

Q: (16) Show that AB=BA for 0 0 0 3 0 0 0 1 A = and B = 0 3 1 2

A: A=-100030001 and B=500030002

Q: 8. Find x in AHJK. K 60° 30° J O 5 V2 O 5 V3 О 10

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Q: dz 14. Evaluate S z(4+2)

A: Given: ∫dzz4+z23. Evaluate the value of the integral.

Q: Evaluate dz (z–2)5/3 O -4/3 O 4/3 O Divergent

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Q: let X be 4-VV flon)= To Finel ECX) oedECXY)

A: f(x) = x/10 where xx = 1,2,3,4

Q: What is/are X-value(s) in ex2-3x+2)= 1? 1 (2,1) none of these O O

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Q: please answer ty

A: As we know that; The sum/difference rule: f±g'=f'±g' The Product rule: f·g'=f'·g+f·g' The Power law:…

Q: Verify S Tokes' Theorem To 2.

A: Introduction: We know that stoke's theorem is given by the formula, ∮CF.dr=∬s2∇×F·n.dσ

Q: Suppose X~N (μ,σ') then X – H - - N (0, 1) o2 O True O False

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Q: n! Verify that Ex1+…+xr=n,xi20 r^n for any r, n>1 x1!x2!...xr!

A: Consider the given information. Let n is greater than equal to 1 arbitrary. Use the mathematical…

Q: O N (AT) = R(A)-

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Q: (a, 0) is not measurable.

A: In this question, we check the given set is measurable or not. here we use the condition of Lebesgue…

Q: (c) Use a calculator to verify that x = 5797, x = 5,606,171, y= 587, y = 67,455 and %3D xy 559,988.…

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Q: An automobile service facility specializing in engine tune-ups knows that 60% of all tune-ups are…

A: It is known that 60% of the all tune-ups are done on four cylinder automobiles, 30% on six engine…

Q: Suppose PRo=62 this means that 38% of observations greater than 62 %3D 80 Select one: O True False

A: Given a statement about P80. We have to choose the statement is true or false.

Q: In yz can be written as : 1 In x - In y + In z a O 4 1. In x- In y- Inz b O 4

A: I have Provided this answer in step-2.

Q: What is KN + IK? GHI J KLM N -4 -3 -2 -1 0 1 2 3 4 KN + IK =

A: It is given that,     We have to find the value of KN+IK.

Q: 10. Show that F; := 2²' + 1 is composite via Pepin's Test.

A: ......(1) Here we are given the 7th Fermat number. We need to show that, 3F7-12≢-1(mod F7)

Q: D. Let Find 2,-

A: We will find out the required value.

Q: Evaluate the following integral 2 πα 3 πα3 na3 3 πα 1 πα3

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Q: 8 Show that 1+2++ In S 1|+ |r2|++|rn| for any numbers r1, 22, ....

A: To show,    x1+x2+.....+xn≤x1+x2+.....xn   for any numbers  x1, x2,....., xn . Which is generalized…