The sum of two numbers is 21. If the product of one of the numbers by the square of the other is to be a maximum, what are the numbers?

Q: The product of two numbers is 4 and the sum of their squares is 8.Find the numbers.

A: Assumption of the numbers and their solution helps to find the required numbers. Addition of the…

Q: The sum of two positive numbers is 4 and the sum of their squares is 28. What are the two numbers?

A: Let the two numbers are x and y.Given that their sum =4 So, x+y=4

Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

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Q: The sum of the digits of a two-digit number is 11. If the digits are interchanged, the new number is…

A: As many Questions are given, I will solve only the first one. Ans 3. Let the digit at ten's place be…

Q: Find two positive numbers that satisfy the given requirements.

A: Let the numbers be x and y,Their product is 147,xy = 147y = 147x              .........(1)given that…

Q: the sum of the three numbers is 2021 . if the smallest of those numbers is reduced by 21 we get…

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Q: The sum of two natural numbers is 61. If one number is five less than five times the other number…

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Q: The sum of two numbers is b. If the product of one number and the other number raised to four is to…

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Q: Find three real numbers whose sum is 9 and the sum of whose squares is as small as possible.

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Q: The sum of two numbers is 1.  What is the smallest possible value of the sum of their squares?

A: Let x be one number, Then other number is 1-x

Q: The product of two consecutive odd integers is 22 less than the square of the greater integer. Find…

A: Given information: The product of two consecutive odd integers is 22 less than the square of the…

Q: The sum of the squares of two positive numbers is 29 and the difference of the squares of the…

A: Suppose that the numbers are x and y. Then given that

Q: The sum of two numbers is b. If the product of one number and the other number raised to four is to…

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Q: A two digit number is seven times the sum of its digits. The number formed by reversing the digit is…

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Q: What is the smallest possible value of the sum of their squares if the sum of two positive numbers…

A: see below the explanation and answer

Q: The sum of two numbers is 15. One of the numbers is twice the second number minus 9. What is the…

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Q: The sum of three consecutive odd integers is 41 less than four times the largest. find the numbers

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Q: The sum of two numbers is 10. What pair of numbers will yield the maximum sum of their reciprocals

A: We have to find the sum of reciprocal

Q: The dimensions of a rectangle with a perimeter of 82 cm if the length is 3 cm less than three times…

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Q: . The sum of two numbers is 21. If the product of one of the numbers by the square of the other is…

A: Given that sum of two numbers is 21. and the product of one of the numbers by the square of the…

Q: The sum of two positive numbers is 40. What are the numbers if their product is to be the largest. A…

A: let the two numbers be "x" and "y "x+y=40 → (1)F(x,y) = xyF(x)= x(40-x)F(x)=40x-x2differentiate…

Q: The perimeter of a triangle is 74 cm. The longest side is 6 cm less than the sum of the other two…

A: Given information: Perimeter of a triangle is 74 cm, Longest side is 6 cm less than the sum of the…

Q: The sum of the squares of two consecutive natural numbers is 313 . Find the numbers

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Q: The sum of the digits of a three-digit number is 8. If the ones and hundreds digits are…

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Q: The sum of two numbers is 120. Find the numbers so that the product of the first number and the…

A: Let's find.

Q: The product of two numbers is 25. What is the smallest possible sum of their squares?

A: Given information: The product of two numbers is 25.  Calculation: Consider x and y are two numbers.…

Q: The sum of a number x and two times the square of a positive number y is 24. Find the maximum…

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Q: One side of a triangle is three times as long as another side, and the third side is 12 inches long.…

A: Let the length of the shortest side of triangle be x inches. given that One side of a triangle is…

Q: Find two positive numbers that satisfy the given requirements.

A: Let x = First number , y= second number   As per given, x3+y=500⇒y=500-x3      (i)

Q: The sum of two positive numbers is 20. Find the product of the two numbers if the sum of their…

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Q: the sum of two numbers is 15.  One of the numbers is twice the second number minus 9.

A: Given: The sum of the two number is 15 and one of the number is twice the second number minus 9. To…

Q: The sum of two positive numbers is 20. Find the product of the two numbers if the sum of their…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: The volume of a rectangular tank is 14 feet less than twice the volume of a cube. The length of the…

A: Consider the length, width and height of rectangular tank be l, w and h respectively. Consider the…

Q: The sum of two numbers is 10. Find the numbers if the sum of their squares is to be minimum given…

A: Given that the sum of two numbers is 10

Q: The width of a rectangle is 6 kilometers less than twice its length. If its area is 140 square…

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Q: The sum of 2 numbers is 45. One number is 4 times as large as the other. What are the numbers

A: Let the numbers be x and y Sum of the numbers is 45 Therefore, x+y=45   ...(1)

Q: A rectangle is three timesas long as it is wide and has the same perimeter as a square whose area is…

A: Let the width of the rectangle is x. According to the question length of the rectangle will be 3x.…

Q: The sum of two positive numbers is 16. What is the smallest possible value of the sum of their…

A: We have to find the smallest possible value of the sum of their squares when the sum of two positive…

Q: The sum of two numbers is 10. Find the maximum product of the first number and the second number.

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Q: The sum of two positive numbers is 24. The product of one and the square of the other is maximum.…

A: Here given that

Q: Thrice the sum of two numbers is 30 and the sum of their squares is 52. Find the product of the…

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Q: There are two more negative even consecutive integers such that the square of the smaller integer is…

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Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

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Q: The sum of two positive numbers is 20. Find the product of the two numbers if the sum of their…

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Q: 7. The sum of the first number and twice the second number is 108 and the product is a maximum. Find…

A: Find your answer below

Q: The average of two numbers is 2x. If one of the numbers is x + 3 , find the other number.

A: We know if average of two numbers = a, then total of these two numbers = 2a.

Q: The sum of one number and three times the second number is 48. What will be the maximum product of…

A: Given that the the sum of one number and three times the second numberis 48.Our Aim is to find the…

Q: If the sum of two numbers is C, find the minimum value of the sum of their squares. A) c2/6 c2/ 4…

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Q: The sum of two numbers is 60 and the difference of those two numbers is 38. Those two numbers are…

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