How many perfect squares are there between 1 000 000 and 9 000 000?

Q: formula for the n^th triangular number is n(n+1)/2. Prove it.

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Q: 's Little Theorm and The Pollard Factorization Metod how could I solve Quetion 4 in Section 6.1

A: Introduction: The product of consecutive integers beginning with that natural number and ending with…

Q: 1. An art student starts with a white, right triangle that has a base of 16cm and heights of 80 cm.…

A: Area of a right angle triangle is 12×Base×Height

Q: The 1st triangular number is 1; the 2nd triangular number is 3; the 3rd triangular number is 6, etc……

A: The solution is given below

Q: How many digits does the smallest positive integer K have, while satisfying all of the following…

A: We will construct the number K bu fulfilling the conditions from bottom to top.

Q: 4 13 a) What is the largest natural number n such that- 11 7 b) Using the ideas from part a, find…

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Q: i. Find the smallest integer K larger or equal to 1+ V53 + 46

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Q: Given 4 numbers with the sum of 9 900 let the second exceed the 1st by 1/7th ,let the third exceed…

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Q: A natural number with 5 as the unit digit is given . when the unit digit is erased , the obtained…

A: A natural number with 5 as the unit digit is given . when the unit digit is erased , the obtained…

Q: (a) Prove, by mathematical induction, that for every positive integer n, 7² r² = (n + 1)² T=1

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Q: 3. The Sierpinski carpet is constructed by removing the center one-ninth of a square of side 1, then…

A: The length of side of original square is 1. So it's area = 1

Q: Find an integer such that its square is 81 less than 18 times the integer

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Q: Find the smallest positive integer N that satisfies all of the following conditions: • N is a…

A: We have to find the smallest positive. N'that satisfies all of the following conditions: N is a…

Q: Q10: The Newton Raphson algorithm for finding the cube root of N is A)를 (x,2 +) B)를 (2x C) (2x+

A: Solution is given below:

Q: TO n. 1+n Let P = 102 then which of the following is/are correct? 2+n 10 +n VA) 2P is perfect square…

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Q: Discrete

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Q: 4. Prove the following showing all the steps below or give a counter example: (a) The difference…

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Q: 2. Find the factors of N = 34571 by computing the values of N+1°, N + 2°, N +3?, N + 4°, … .. until…

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Q: For the natural numbers that are multiples of 3 and less than 76. a. What is the largest of these?…

A: The natural number that are multiple of 3 and less than 76 are  3,6,9,12,........,72,75

Q: Show that we can easily factor n when we know that n is the product of two primes, p and q, and we…

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Q: 5.( Use the methods of this class to find two numbers, x and y, whose sum is 10 and with the…

A: A series is the set of numbers may be related by some rule, which is not a necessity. Series may be…

Q: Q1. Find the square root of the following by prime factorization. [1] 20.25…

A: according to rules of Bartleby i am solving only question number-1, kindly repost other questions as…

Q: I am a positive integer. All my digits are odd. I am equal to the sum of the cubes of my digits.  I…

A: There are two possible answers for the given situation.If it is a single digit number, then it…

Q: Prove that the sum of n squares can be found as follows n(n + 1)(2n + 1) 12 + 22 + 32+..+n? 6

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Q: x+(x+1)+(x+2)+(x+3)+(x+4)=5x+10 What does this prove about the sum of these natural numbers?

A: The sum of the given equation is calculated as follows.

Q: Denote by an the nth positive integer that is not a perfect square. For example, we have…

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Q: Show that the sum of the squares of the first n natural numbers is given by,S=(n(n+1)(2n+1))/6

A: We have to show that the sum of the squares of the first n natural numbers is given by S=nn+12n+16…

Q: A student claims that V80 is in the simplest radical form. Which statement is true? The claim is…

A: the prime factorisation of 80 is : 80= 2*2*2*2*5 ∛80=∛2*2*2*2*5        =2*∛10 hence this is the…

Q: Determine how many terms of (-1)*+12k k! must be summed to be sure that the remainder term k=1 is…

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Q: box with a square base and no top is to be made from a square piece of carboard by cutting 2 in.…

A: Let x be the length of one side of the cardboard. So, the initial piece of cardboard is x by x. If 2…

Q: Find the largest negative integer leaves a remainder 2 when divided by 3, 5, and 12. (If it is not…

A: Let us  solve the question in the next step.

Q: 6. Find the remainder when 721 divided by 43 7. For a given integer n, prove that 3 k-0

A: To find the remainder when 7221 divided by 43. Now, 7 and 43 are relatively prime and 43 is a prime…

Q: k 22. k+1 k31

A: For the part circled in pink, can you show where the k^3 came from in the numerator? (Under square…

Q: We say two numbers m and n are consecutive perfect squares when m is the square of a positive…

A: We need to find year when men was born.

Q: Use Polya’s Four Steps to solve the following problems. 1. ) Susie’s age this year is a multiple of…

A: We will use Polya's four steps method:

Q: 1. Prove that the sum of the consecutive cubes is given by this formula: n²(n+1) 4 13 + 23 + 33 +..+…

A: Given; 1) 13+23+33+...+n3=n2(n+1)2/4 Repost the next questions.

Q: 6. Find the root using Regula-Falsi Method a) x* -x- 10 = 0 Ans. x = -1.697 and 1.855

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: 4 (a) Write out the multiplication table for Z6. How many times does [0]6 appear in each row of the…

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Q: The following rectangle is being enlarged by a scale factor of 150%. What is the perimeter and aread…

A: Given The given rectangle is The rectangle is enlarged by a scale factor of 150%.

Q: 5. Find the 45th term of the pentagonal numbers {1, 4, 12, ...}. Show how you get your answer here:

A: We know, The nth pentagonal number is given by Pn = n(3n-1)/2   Here P1 = 1(3*1-1)/2 = 1 P2 =…

Q: the sum. In the tile pattern below, the first block affangement has 1 block, the second block…

A: Please see the explanation below

Q: Q: Is there a formula to get the square root and cube root of a number manually without using a…

A: Is there a formula to get the square root and cube root of a number manually without using a…

Q: 60. For what positive integer k is k+5 a factor of k2+11 while k+11 is a factor k2+5? ANS. 7

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Q: 8. The number is such that when it is divided by 8, it gives a perfecct cube but not a perfect…

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Q: Find the least positive integer n for which 2n + 5n - n is a multiple of 1000.

A: To find the least positive integer n for which the expression 2n +5n-n is a multiple of 1000.

Q: Using the Error Approximation discussed in class, the smallest integer N for which 16 < .08 is n=N…

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Q: Suppose n is odd. Find the cube of n and divide it by 4. What possible remainders could occur? Check…

A: Solution

Q: 5 of 15 Two similar rectangles have a scale factor of. How much larger is the area of the larger…

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Q: Find the smallest positive integer N that satisifies all of the following conditions N is a square…

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Q: The teacher wrote the three-digit number  he imagined on the board. Three students made two…

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