Find two positive integers such that the sum of the firstnumber and four times the second number is 1000 and theproduct of the numbers is as large as possible.

Q: Find three consecutive even intergers such that the product of two smaller numbers is the same as…

A: Let the consecutive even integers be  x, x+2,x+4, where x  is even , then we use the given condition…

Q: Find two positive numbers, x and y, whose sum is 100 and whose product is as large as possible.

A: Let the two positive numbers are x and y. Now, Their sum is 100. That is,          x+y=100⇒y=100-x

Q: Find the two positive integers whose sum is 16 and the sum of whose square is minimum

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Q: Find three consecutive even integers such that the sum of the squares of the first two is four less…

A: Let the three consecutive even integers are n , n+2, n+4

Q: Find two positive integers whose sum is 16 and the sum of whose squares is minimum

A: Given sum of two numbers are 16. Let first number be x and second number=16-x. Now, sum of squares…

Q: Find two positive integers such that the sum of the first and five times the second number is 2000…

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Q: Find three positive numbers whose sum is 36 and such that the sum of their squares is as small as…

A: Solution is given below:

Q: Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of…

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Q: The product of two positive integers is 30, and their sum is 17. What are the integers?

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Q: Suppose a hiker finds himself in a forest 4 miles from the nearest point on a straight road. He…

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Q: Find two positive real numbers such that the sum of the first number squared and the second number…

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Q: Find a positive number such that the sum of the number and its reciprocal is as small as possible.

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Q: Find the positive integer that maximizes the sum of the numbers and its reciprocals?

A: First make equation and then differentiate

Q: 12. Of all numbers whose sum is 70, find the two that have the maximum product.

A: let x and y be two numbers whose sum is 70   we have to maximize  M=xy where x+y=70

Q: Find three positive numbers whose sum is 48 and such that their product is as large as possible.…

A: The solution to the given question is explained below. We use partial differentiation technique to…

Q: Find a positive number for which the sum of its reciprocal and four times its square is the least.

A: Let x be a number. According to question

Q: Find two positive numbers such that the sum of twice the first number and three times the second…

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Q: Find the minimum sum of two positive numbers (not necessarily integers) whose product is 200.

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Q: Find the number in the interval [ - 5,5] so that the sum of six times the number and its square is…

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Q: Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible.

A: To find a positive number for which the sum of it and its reciprocal is the smallest possible.

Q: Find the smaller of two consecutive integers such that twice the smaller exceeds the larger by 10.

A: We can solve the problem by taking the smaller one as x and the larger one as x+1.

Q: Find two non-negative numbers such that the sum of two times the first and three times the second s…

A:

Q: Find three consecutive odd intergers such that the product of the two larger numbers is 18more than…

A: To form the equation satisfied by the required integers  and therby solve for them

Q: Find two positive real numbers such that they sum to 108 and the product of the first times the…

A:

Q: Find three positive numbers that sum to 150 with the largest possible product of the three.

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Q: . Find two positive integers such that the sum of the first number and four times the second number…

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Q: Find three positive numbers that sum to 150 with the greatest possibleproduct of the three.

A: Given: we to find three numbers that sum to 150

Q: Find two nonnegative numbers such that the sum of first number and 3 times the second number is 1200…

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Q: Find three consecutive odd integers such that the product of the first two is 52 more than the third…

A: Let the three consecutive odd integers are  n-2, n and n+2 So as per question, product of first two…

Q: 3. Find two positive read numbers such that the sum of the first number squared and the second…

A: Let the numbers are x and y. x2 + y = 48 .................(1) y = 48 - x2   The product of two…

Q: Find two nonnegative numbers such that the sum of first number and 4 times the second number is 1600…

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Q: Find two consecutive integers such that tn more than twice the smaller is seven less than three…

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Q: Is a product of two positive decimals each less than 1 always less than each of the decimals?

A: To state the give statement is true or false.

Q: find two positive numbers whose sum is 300 and whose product is a max

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Q: Find the two consecutive positive integers such that the square of the first is decreased by 17…

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Q: the number and its reciprocal.

A: Given: The smallest sum of a number n and its reciprocal 1n is 2 which occurs when n=1. Any other…

Q: The mean of 5 positive integers is 16. What is th maximum value that one of this numbers may have?

A: Given problem is :

Q: Find three positive numbers whose sum is 63 and such that their product is as large as possible.…

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Q: Find two positive integers such that the sum of the first number and four times the second number is…

A: Given: The sum of first number and four times the second number is 1000. The product of two numbers…

Q: Find two integers whose sum is 140 and whose product is as large as possible.

A: Topic=Algebra Two integers are 70 and 70.

Q: Find the three consecutive integers such that that product of the first and third is one less than…

A: Take three consecutive integer as below :n-1, n , n+1

Q: Find two positive numbers such that the sum of the first and twice the second is 72 and whose…

A: Given the two positive numbers such that the sum of the first and twice the second is 72

Q: Find two positive numbers such that the sum of the first and twice the second is 96 and whose…

A: Let the first number be "x" and the second number be "y". The sum of the first and twice the second…

Q: Find two positive integers such that the sum of the first number and four times the second number is…

A:

Q: Find the three positive numbers whose product is 27 such that their sum is as small as possible.

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Q: Find a positive number such that the sum of the number and its reciprocal is as small as possible

A: Second Derivative Test :   Firstly find critical point of f(x).i.e, f'(x)=0 and find the value of…

Q: Find a pair of non-negative numbers that have a product of 162 and minimize the sum of two times the…

A: Let the numbers be x,y. Given  x·y=162y=162x The function to be minimized will be Fx=2x+y…

Q: 11. Determine three positive numbers whose sum is 21, so that your product is the maximum possible…

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Q: Find three positive numbers whose sum is 400 and whose product is a maximum. Answer (separate by…

A: Let the three numbers be x, y, z. The sum of numbers = 400. Therefore, x+y+z= 400.…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.