Given that z = V3+i. (a) Find z10 and express your answer in the form a + ib, where a and b are real numbers. (b) Find the integers n for which z" is a real number.

Q: To find the answer to a probelm such as 2+8 (x-1),what would be the first step?

A: Follow the procedure given below.

Q: If h(t) t" where n is a natural number, then what is h'(t)?

A: If h(t)=tn, where n is a natural number then our aim is to tell the valueof h'(t)=?

Q: Solve the following equation with master theorem  T(n) = 2T(n/2) + n2

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Q: Do not use a calculator in this question. (4 V5 – 2)? V5 – 1 CamScanner로 스캔하기 Express in the form…

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Q: These equations can be solved to give [Q] [0.7321 0.2679 0.1964 0.0714 0.0536 0.0178]. comoo 200--0

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Q: If m and n are integers and m x n = 0, then what is true for the values of m and n?

A: If m and n are integers and m×n=0

Q: Find all solutions to 2sín (20)-12=0 on the interval

A: Solve using basic of all silver tea cups graph for trigonometry quadrants .

Q: O Calculate the d eterminant of [I 30 2 -2 -5 7 4 3521 7-1 2 -3

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. What is the coefficient of x? a) in (1 + 2x)117 b) in (2 – x)13? c) in (5 – 2x + y)'1, where y is…

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Q: Find the value of a so that V1-x² O 1 2 O 3 2

A: SOLUTION-

Q: Let floor(1) + floor(1/2) + floor(1/3) + …· + floor(1/n) = ceiling(0/1) + ceiling(1/2) +…

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Q: 3/2n 7. Find proj in terms of: (a) b)

A: Solution of the problem as follows

Q: Determine the general solution of the following Efuler equatión for x>°, g-2xy-4y= \0x using the…

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Q: d x" = nx"-1 de 4. Prove that NɛQ

A: ddxxn=nxn-1 ;   n∈Q

Q: Find the solution for an = an-2 for n22 and ao = 5, a1 = -1.

A:

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: If x is any real number, then cosh x Σ n=0 n! + 198 Σ n=0 (-x)" n!

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Q: 2. Find x in b = ax if a=23 and b=368. Reply in this format: 1. q = r = 2. x =

A: The given expression is: b=axwhere:a=23        and       b=368

Q: What is the principal argument of z = 3 + V3i?

A: Let z=x+iy be a complex number. Then, the polar form of z is given by, z=rcosθ+isinθ where…

Q: Which of the following is not a proposítion? A 2x+5=4x+5 when x=0 B 55=4x+5 where x = 10 %3D y=4x+5…

A: The proposition in math is a statement which can not be decide whether it is true or not.

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

A:

Q: For which values of a does ax = 1 have a solution in Z5?

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Q: For any numbers a andb and an even natural number n, show that the equation x" + ax + b = 0, x in R,…

A: Here, to prove this result we have to use Rolles theorem.

Q: Solve the following equations in Z6 with x expressed in both standard and non-standard names: (i) xx…

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Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: don't understand how you did this answere? Ppiranha=npiranhanTotal=724=

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Q: (i) Show that (5 + 3v2)² = 43 + 30v2. Hence find, without using a calculator, the positive square…

A: As you didn't mention the question numberto be solved so i solved First 3 question.For remaining…

Q: of t/4 for x. (If an answer is undefined, enter UNDEFINED.)

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Q: у" — бу" + 11у' — бу — 4sin7х + 5 - %3D -

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Q: 2 Xi. にく prove thate 2.

A: Given that  We have to prove the given expression:

Q: 5) Let A= 18 Using Caley-Hamilton theorem find the expression A* -19A³ + 18A? + A + 21.

A: Please refer the attached image for complete solution.

Q: Q4: Answer two only: 4 2 2 -2 Find AB and AC. A): If A = 01 0; 1 -1 1. 2 B = 2 -1 3 -2 2 4-1711 -2…

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Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              => k(15 - 13) = 2k for any integer k              => 15 k -…

Q: In the given figure, PR is 12 more than twice PQ, and QR is two more than four times PQ. If all…

A: Given: In the given figure PR is 12 more than twice PQ, and QR is 2 more than 4 times PQ. To Find:…

Q: e3x + 6 enx e(n+1)x = 1+ e® + 2 Sx n! (n+ 1)!

A: The given series is : eex=1+ex+e2x2+e3x6+·····+enxn!+en+1xn+1!   Let fx=ex The above function can be…

Q: x² + 6x – 1

A: We have to express  x2+6x-1 in the form (x-m)2+n.

Q: 8. Determine the value of k, given that: (x -k) dr=0 (3x +1)(r+1)

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: The sum of values of x for which the equation x0929 + x. 3o92 * = xl092 15 holds true is

A: The graph is shown below:

Q: Q2) n(x) = x-1 , k(x) = (x – 1)/2, mx) = (x + 8)¯1 (x + 8)-1 Find a formula for ( m onok).

A: See answer below.

Q: Prove that tanodo-n//2.

A:

Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: Prove that there are no solutions in integers x and y to the equation 2x2 + 5y² = 14.

A: Two different proofs are given for the given problem as follows :

Q: How many solutions are there to ax + b = 0 with a 0?

A: Given  ax+b=0   ;  a≠0

Q: 9. In OP, QR = 7x – 20 and TS = 3x. What is x? -

A: Joining QP and TP, we get the radius of the circle.

Q: find the seves Roc and IOC ("! )³ (a) (b) nニ1 n=0 3

A: (a) The given series is ∑n=1∞n!22n2n!xn. We will first evaluate the limit limn→∞an+1an. In our…

Q: and (A) (B) = x, = 2x, = 3x, Show that if 8. N N (AB) _ (BC) _ (AC) 1 = y, then the value of neither…

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Q: 2. 2. (xij-X-) Xij-.. prove thate

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Q: For which values of a does ax = 1 have a solution inZ6?

A: Z5=0,1,2,3,4,5ax=1If a=0, then 0x=1⇒ No solution.If a=1, then 1x=1⇒One solution,x=1

Q: -X+5 SY STEM= ** -*+Sy SY STEM = + bt) -t

A: This is a problem of differential equation.

Q: Find the interval (a, a + 1) for integer value a for which e- = 2x + 3 has a solution.

A: