The number a gives residue 15 in division with 77 and the remainder 16 in division with 78. What residue does a give in division by 14?

Q: 4063 Find (with proof) the residue of 3200s when dividing it by 93.

A: Euler's phi function is very significant in calculating the residue. As Fermat's little theorem is…

Q: Simplify by reducing the index of the radical ^6sqrty^3

A:

Q: For what value of b is this expression NOT FACTORABLE (prime)? x2 + bx + 36 Ob = 13 %3D Ob = 12 Ob =…

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Q: Justify whether it is true to say that the given is the nth term of an AP  1+n+n2

A: We have to say that whether the given nth term is in A.P. where, 1+n+n2 We have given nth term of…

Q: (c) Use Euler's Theorem and part (b) with a suitable value of p to find the remainder of 5103 when…

A:

Q: Determine the coefficient of a° in (1– 5a³)® by completing the following given steps.

A: we have to determine the coefficient of a3 in 1-5a35. as we know that if we have (x+y)n then the…

Q: 2.269910988417 x 10^23 so what will i use to bring it down to under 100 ? how to divide it ?

A: so to bring it down 100 we just divide it by number x we now have to find the value of x

Q: express each of the following as a single fraction involving positive exponents only. 3a-2 + 4b-1

A: The negative exponents can be converted to positive exponents by taking the reciprocal of the…

Q: The remainder upon the division of x75 + 6 by x – 3 in z, is: O 1 O 5 O 6

A: Objective is to find the reminder.

Q: · Find (with proof) the residue of 320222022 when dividing it by 31.

A:

Q: If x is positive, the first negative term in the expansion of (1 + x)27/5 is (a) 5th term (b) 6th…

A: Introduction :

Q: Find the exact value of the expression.

A:

Q: 2) Rewrite each of the following using rational exponents.

A: (n√x)m = (x1/n)m = x1/n × m = xm/n Where m, n and x are integers

Q: (b)If x is so small that its fourth and higher powers may be neglected show that (1 + x) + V(1- x) =…

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Q: The remainder upon the division of x98 + 4 by x – 2 in Z, is: O 1 O 5 None

A: Find zero of x-2 and use it to solve given problem.

Q: 6. Find the remainder of 17036543 on division by 25.

A: Thus, remainder = 2

Q: 5 find the quotient i15-as a" by long division meth od 1-a

A:

Q: Show that n22-1 is division by 8, if n is an odd positive integer

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Q: Show that n2-1 is division by 8, if n is an odd positive integer

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Q: Simplify expresson. the radical 6. a

A:

Q: 44. Rewrite each of the following as an equivalent expres- sion with a rational exponent. [R.5] а)…

A: since you have posted multiple questions, so I'll solve first three for you , for rest question's…

Q: express each of the following as a single fraction involving positive exponents only. x-3 - y-1

A: we have to express x-3-y-1 as a single fraction involving positive exponents only

Q: A man on the 13th floor of a building sees a bucket (dropped by a window washer) pass his window and…

A:

Q: Find (with proof) the residue of 32022-022 when dividing it by 31.

A:

Q: express each of the following as a single fraction involving positive exponents only. 2x-1 - 3y-2

A: Given: 2x-1-3y-2

Q: Consider the remainders when dividing by 12. Which of them will be included in the group of…

A: We need to consider the remainders when dividing by 12.  The answer -> Multiple Solutions are…

Q: 1. Find the remainder when 53751 is divided by 11.

A: 1. We will use the Euler's theorem, to find the remainder.

Q: use the Euclid's division lemma to show that the cube if any positive integer is either of the from…

A:

Q: A man on the 15th floor of a building sees a bucket (dropped by a window washer) pass his window and…

A: A man is on the 15th floor.  Height of a floor: 14 ft. Assume: window is in the middle of the floor.…

Q: the periodic decimal 0.110110110110110...(continuing on in this pattern forever) as a ratio of two…

A: Given, the periodic decimal                                0.110110110110110...

Q: express each of the following as a single fraction involving positive exponents only. x-1y-2 - xy-1

A: Consider the expression, x-1y-2-xy-1

Q: Show how Newton's method could be used to find bm for b > 0, where m is a positive integer, without…

A: In this question, we need to write the numerical  scheme to find the mth root of b>0 i.e b1/m we…

Q: What is the length of BD? Write your answer as an integer of exact radical. 2 A

A:

Q: Find the indicated real nth root(s) of a. n = 4, a = -81 O +3 -/3

A: This question is about nth real roots of numbers

Q: (3x+4) (2x+4)     but with each as a radical.    Is it possible to multiply each if they are a…

A: Yes, you can multiply them if they are radical by using this basic law of radicals:

Q: If You are asked to prove the Lagrane form of the remainder? How would you do that?

A: I assumed that,you are asking  lagrange's form of remainder.instead of Lagrane. So, we have to prove…

Q: The remainder upon the division of x + 4 by x – 4 in Z, is: 1. None

A:

Q: 24/0.96 its dividing by two digits but idk how to do it

A: In the question we have to divide the given numbers.

Q: . Find (with proof) the residue of 3200 when dividing it by 93.

A:

Q: Given 1. x√3x 3 64 2. √121 3. √5x4 nd and the index of each radical. Radicand Index

A: To find the radicand and the index for each radical. Note that: qp is called a radical expression in…

Q: State the steps you will take to transform  3x + n = 7 to  x = (1/3)[7- n]

A: Given, 3x + n = 7 to  x = 13[7- n] step for the following transformation is as follows.

Q: Given q Is it easier to evaluate q(1) by using synthetic division or by direct substiItution? Find…

A: Put value in function

Q: Find the expression of 1/(2+5x)3 , magnitude of 5x/2 < 1, in ascending powers of x up to and…

A: Compare as expansion of (1+x)^n

Q: Show that n22-1 is division by 8, if n is an odd positive integer

A: If n is a odd positive integer n can be written as   n = 2k+1 by substituting in n2-1 n2-1 =…

Q: Express the following fraction in simplest form, only using positive exponents. 20y²h-1 (5y h2)2

A: We have to simplify the following expression into simplest form using only positive exponents.…

Q: find the simple formula for the product (1-1/2)(1-1/3)...(1-1/n)

A: topic - product of series  answer is 1/n

Q: find the rational number represented by the repeating decimal. 0.451141414

A:

Q: 10. When ax -+ 2x +bis divided by x-1, the remainder is 10. When it is A divided by x-2, the…

A: Given : f(x) = ax³ - x² + 2x + b

Q: Find (with proof) the residue of 320222022 when dividing it by 31.

A: Given number is 320222022 Let the remainder(residue) be x when 320222022 divide by 31 x=32022202231…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.