Find three positive numbers whose sum is 36 and such that the sum of their squares is as small 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 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 such that the sum of the first and five times the second number is 2000…

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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 digit of positive integer, having three digits are in AP. And are their sum is 15. The number…

A: given that three digits sum is 15number obtained by reversing the digits is 594 less than the…

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

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Q: Find two numbers whose sum is 40 and whose product is a maximum.

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Q: product

A: We will solve the problem.

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 two numbers whose sum is 60, such that the sum of the square of one number plus twelve times…

A: Let the two numbers are x and y. Sum of two numbers is 60. x+y=60                                ⋯1…

Q: Find two numbers whose sum is 20, if the product of one by the cube of another is to be the maximum.

A: For stationary value of a function y = f(x),   y' = f'(x) = 0  A function y = f(x)  is said to have…

Q: Verify that for any three consecutive integers, the sum of the smallest and largest is equal to…

A: Given: Three consecutive integers.

Q: The product of two positive numbers is 16. Find the numbers if their sum is least.

A: Given the product of two positive numbers is 16

Q: The product of two positive integers is 112, and their sum is 22. What are the integers?

A: Since, we have been given that the product of integers is 112 and their sum is 22.Let 'x' and 'y'…

Q: Find two numbers whose sum is a if the product of the square of one by the cube of the other is to…

A: Consider the first number be 'x'. The second number be 'y'. The sum of the numbers is given by a.…

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 numbers whose sum is 9 if the product of one by the square of the other is a maximum

A: Explanation of the answer is as follows

Q: Find two positive numbers the sum of which is 100, and the square of one number times twice the cube…

A: Use the given statement mathematically then solve by making the function and make derivative of that…

Q: Find three consecutive even integers such that three times the sum of the smaller two integers is 22…

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

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Q: Find two consecutive positives even interfere such the sum of their squares is 52?

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Q: Find all pairs of numbers that satisfy these two conditions: Their sum is 20 and The sum of their…

A: This question is related to numbers,  We will solve it using given information.

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 real numbers x and y whose sum is 36 and whose product is as large as possible

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Q: Find two numbers whose sum is 20 and whose product is a maximum

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

A: Suppose x and y be the positive numbers whose product is 100 So, xy=100 Then, y=100x…

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

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

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Q: Find three real numbers x, y, z whose sum is 6 and the sum of whose squares is as small as possible.…

A: Suppose the numbers are x,y and z which sum is 6. So, g(x,y,z)=x+y+z-6=0...(1) And, whose sum of…

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 the three positive numbers whose sum is 48 and whose product is as large as possible.…

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

A: Let the first number be x. Let the second number be y.   Given: x+4y=1000x=1000-4y   Determine the…

Q: Find two numbers whose sum is 50 such that the square of one number plus six times the other number…

A: Let 'x' be the one number and the other number is (50-x).

Q: Find the two numbers whose sum is a. If the product of the square of one by the cube of the other is…

A: Let us consider the function f(x)  To maximize the function  Differentiate the function with…

Q: The product of two positive numbers is 363. Minimize the sum of the first and three times the…

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Q: Find two numbers such that the sum of the first and twice the second is 56 and whose product is…

A: Sum of the first and twice the second is 56.

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

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Q: Find two positive numbers whose sum is 84 and whose product is as big as possible.

A: It is number Problem.

Q: Determine what will be the three positive numbers that its product is 27 and its sum is as small as…

A: We will find the three numbers satisfying the given conditions.

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 two numbers whose sum is 11 and whose product is a maximum.

A: Let x and y be the two numbersx+y =11y =11-xProduct is maximumTherefore, xy is maximumx(11-x) is…

Q: The product of two positive numbers is 185. The smallest possible sum of those number is

A: Since,The prime factorization of 165 is 1Q5 =1X5 X37=5X37 ----1 From 1 it is clear that the two…

Q: Divide the number 120 into two parts such that the product of one part and the square of the other…

A: To divide the number 120 into two parts such that the product of one part and the square of the…

Q: Find two positive real numbers whose sum is 40 and whose product is a maximum.

A: A function f(x) is said to have a maximum value at a point c when the first derivative of the…

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.

A:

Q: Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given…

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