Find two positive numbers if the sum of the first number and twice the second number is 108 and the product is a maximum. (Input numerical values only, do not type the units, space or comma.)

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 positive numbers whose sum is 45 and such that their product is as large as possible.…

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Q: Find the two positive numbers, whose product is 100 and sum is maximum.

A: We have to find the two positive numbers, whose product is 100 and sum is maximum.

Q: Find two positive numbers x and y whose product is maximum and 2x + y = 100.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Divide 120 into parts so that the product of one and the square of the other is maximum, find the…

A: Consider the two numbers be 120-x and x. Consider the function fx be product of 120-x and x2.…

Q: Find the dimensions of a rectangle with area 216 m2 whose perimeter is as small as possible. (If…

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Q: Find the maximum number of goldfish you can put in a cylindrical tank whose diameter is 8 meters and…

A: Fish would be put in the tank, that is, the volume of the tank. Hence the volume of the tank helps…

Q: The sum is 110.Find two positive real numbers whose product is a maximum.

A: Given: The sum is 110.

Q: ) The length of the box is 9 inches more than its width. The height of the box is 1 inch less than…

A: Given: Length is 9 inches more than width. Height is 1 inch less than width. Volume = 72 inch3

Q: A rectangular garden is 5 ft longer than it is wide. Its area is 6000 ft². What are its dimensions?…

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Q: The difference of two numbers is 22. Find the numbers so that their product is to be minimum.

A: Numbers

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 perimeter of a rectangle is 48 cm. Find the lengths of the sides of the rectangle giving the…

A: Let the two adjacent sides be a and b  Perimeter of Rectangle P = 2 ( a + b ) 48 = 2 ( a + b ) a + b…

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 two positive numbers whose product is 289 and whose sum is a minimum. List them in…

A: as per the guidelines we can provide solution to one question at a time , you can repost the other .

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: The length of a rectangle is 5 cm less than twice the width. Express as an integer the maximum width…

A: here, objective is to find the maximum width of the rectangle for which perimeter is less than 84c.m

Q: Find the dimensions of the rectangle with perimeter 153.6 millimeters with the largest possible…

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Q: Find two positive numbers that satisfies the given requirements. The product is 147 and the sum of…

A: This is an optimization problem in which product = 147 is equality type constraint and function is…

Q: The sum of the first and three times the second is 42.Find two positive real numbers whose product…

A: This question is taken from the application of derivative in which we have to find the two positive…

Q: Find two positive numbers that satisfy the given requirements. The sum of the first number squared…

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Q: 120 into two parts so that the product of one and the square of the other is maximum. Find the…

A: We will find the numbers.

Q: 1500 square centimeters of material is available to make a box with a square base and an open top,…

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Q: A rectangle has perimeter 42 feet and an area of 98 square feet. Find the dimensions of the…

A: Let x be the length of the rectangle and y be the width of the rectangle.Given, Perimeter of…

Q: Find three positive numbers whose sum is 260 and whose product is a maximum. (Enter your answers as…

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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: Among those positive real numbers x and y whose sum is 50, find these numbers that makes their…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 7. The diagonal of a certain rectangle is twice its length minus 2₁ while its width is twice its…

A: Given d=2(l-2) W=2(l-8) Area=? Perimeter=?

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

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Q: Find the dimensions of the rectangle that'll give the max rectangle area, of perimeter of entire…

A: The perimeter of the entire figure is 12 feet.

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

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

A: Here we use application of derivatives.

Q: An open-top box is to be made from a 37 in. by 27 in. piece of cardboard by removing a square from…

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Q: Find two numbers whose sum is 14 and whose product is the maximum possible value. What two numbers…

A: Given the sum of the two numbers is 14

Q: Among all pairs of numbers (x,y) such that 2x+y=17, find the pair for which the sum of squares,…

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Q: Find two positive numbers whose product is 192 and the sum of the first and three times the second…

A: Suppose two positive numbers are  x and y The product of numbers are 192 therefore, xy=192 ⇒y=192x…

Q: Find the two positive numbers whose product is a maximum and the sum of one is five times the other…

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Q: Find two positive real numbers whose product is a maximum. The sum of the first and three times the…

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Q: Find two positive numbers whose product is 36 and whose sum is a minimum. (smaller number) (larger…

A: Our Aim is to find two positive numbers whose product is 36 and whose sum is a minimum.Let 'x'…

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: 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 numbers whose product is 250 such that the sum of the first and four times the…

A: Let the two numbers be a & bHence, ab = 250Hence, b = 250 / a

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

A:

Q: Find two positive real numbers whose product is a maximum. The sum of the first and three times the…

A: Here, we need to find two positive real numbers whose product is a maximum. The sum of the first and…

Q: Find two positive numbers that satisfy the given requirements. The product is 147 and the sum of the…

A: Let x and y be the required numbers. Now given that the product is 147. That is,

Q: Find two positive numbers whose sum is 9 and the product of one number and the square of the other…

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Q: The length of the rectangle exceeds its breadth by 3 cm. If the length and breadth are each…

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Q: A large plywood box has a volume of 12 ft3. Its length is 4 ft greater than its height, and its…

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