The sum of two numbers is k. What are the numbers if the product of the first by the cube of the other is maximum?

Q: The sum of the bases and altitude of a trapezoid is 36 inches and one base is 6 inches longer than…

A: We have to find all three dimensions

Q: You are given a real number N. How should you write it as a sum of two real numbers so that their…

A:

Q: The sum of the first and twice the second is 360 and the product is a maximum.

A:

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

A:

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

A:

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

A: Numbers

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

A:

Q: A number of two digits exceeds twice the sum of its digits by 26. If the digits are interchanged,…

A: Given,         A number of two digits exceeds twice the sum of its digits by 26. If the digits are…

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 design of a digital box camera maximizes the volume while keeping the sum of the dimensions at…

A: Explanation of the solution is given below....

Q: The sum of the first and twice the second is 24.Find two positive real numbers whose product is a…

A: given,       The sum of the first and twice the second is 24

Q: The sum of two numbers is 60. The product of one by the cube of the other is to be a maximum. What…

A: We have to find the numbers

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: An oil-producing country can sell 7 million barrels of oil a day at a price of $110 per barrel. If…

A:

Q: Find two numbers whose sum is 10, and the sum of whose squares is a minimum. Please put the…

A:

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: The number 72 is to be represented as the sum of two positive parts, such that the product of one of…

A: Let the two numbers be: x and y Therefore we have to maximize:  f(x, y)=x y3 subjected to…

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

A: This question is about sum and product of 2 numbers & to find maximum.

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: . 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: Find two numbers whose sum is 15, if the product of the square of one by the cube of the other is to…

A: We have to fine two numbers for given conditions.

Q: Find a pair of numbers such that the sum of the first number squared and twice the second number is…

A: Find a pair of numbers such that the sum of the first number squared and twice the second number is…

Q: The sum of two numbers is 12. if one number is x, what is the value of x such that the product of…

A: Here, let the two numbers be: x & y Then, x+y=12⇒y=12-x Now, the product of the two numbers be:…

Q: The sum of the squares of two positive consecutive even integers is less than two more than ten…

A: Topic: Algebra Consecutive numbers that follow each other in a sequence. The square of a number is…

Q: The perimeter of a rectangle is to be no greater than 80 centimeters and the width must be 10…

A: let length be x and width is given to be 10. Perimeter of a rectangle is defined as 2(length +…

Q: Twice the smallest of three consecutive odd integers is five more than the largest integers.

A: Given that:-There are three consecutive odd integers.Twice the smallest integer is five more than…

Q: the sum of two positive integers is 24. Find the number if the sum of their squares is a minimum

A: Given- The sum of two positive integers is 24.  To find- The number if the sum of their squares is a…

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…

A:

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 number is 10. Find these numbers if the sum of their squares is a minimum

A:

Q: The sum of the bases and altitude of a trapezoid is 36 inches and one base is 6 inches longer than…

A: Here we use the application of derivative.

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.

A:

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

A: This is s language problem

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

A:

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

A:

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

A:

Q: The sum of two nonnegative numbers is 20. Find the numbers if one number plus the square root of the…

A: according to given problem x+y=20x+y=b

Q: The sum of two positive numbers is 18. What is the smallest possible value of the sum of their…

A:

Q: . Find two numbers whose product is 64, and whose sum is a minimum. 2. The sum of two numbers is…

A:

Q: 2. The sum of two numbers is 12. Find the two numbers if the sum of their squares is to be a…

A:

Q: In planning a restaurant, it is estimated that a daily profit of $6 per seat will be made if the…

A: Let x be the number of seats that is beyond 50 seats, Then the daily profit per seat is decreased by…

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

A:

Q: A number with two digits is equal to four times the sum of its digits. The number formed by…

A: Let x be at the unit place and y is at the tens place. So, the original number is: 10y+x The…

Q: The sum of two numbers is 26 . Find them if the product is to be maximum

A:

Q: What are two numbers whose sum equals to 23, and whose product is a maximum

A: Let the two numbers be x and y.