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What is the link between the product of any four consecutive positive integers and some square numbers?
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
What are two numbers whose sum is 120 such that the product p of one number and the square of the remaining number is a maximum?
To find the numbers that maximize the product p, we can use the formula for a quadratic equation: x = -b / 2a. Let's call one number x and the other number (120-x). Therefore, the equation becomes x(120 - x^2), which simplifies to -x^3 + 120x. We can find x by setting the derivative equal to zero, resulting in x = 10. Therefore, the two numbers that maximize the product are 10 and 110, with a product of 12100.
What are the 2 numbers whose product is one called?
Numbers whose product is one is called multiplicative inverses.
Reasons why square numbers are said to be composite numbers?
Prove the opposite.Assume that a square number is prime.A square number is one that is a product of a number multiplied by itselfA prime number is one that has no factors other than itself and 1.For a prime number to be square, the only choice is for it to be 1*1=1Since 1 is not a prime number, there is a contradiction, and the original premise is false.Therefore, all square numbers must be composite.â–
When the square root of one number is multiplied by the square root of a second number the product is the square root of 36 one of the numbers is not 1?
If the two numbers are a and b, then: √a √b = √(ab) = √36 → ab = 36 So any two [positive] numbers whose product is 36 will be a solution, except the pair 1 and 36 as that has been specifically excluded; thus possible solutions are: √4 x √9, √2 x √18, √(1/2) x √72, √(1/4) x √144, etc. (The first one being the only solution where the square roots are whole numbers.)
What is the link between the product of any four consecutive positive integers and some square numbers?
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
The product of fifteen consecutive whole numbers is 0 what the greatest possible sum of the whole numbers?
For the product to be zero, one of the numbers must be 0. So the question is to find the maximum sum for fifteen consecutive whole numbers, INCLUDING 0. This is clearly achived by the numbers 0 to 14 (inclusive), whose sum is 105.
What is 2 non zero numbers whose product is one?
If the product of 2 numbers is one, than those 2 numbers are recipricals
What are two numbers whose sum is 120 such that the product p of one number and the square of the remaining number is a maximum?
To find the numbers that maximize the product p, we can use the formula for a quadratic equation: x = -b / 2a. Let's call one number x and the other number (120-x). Therefore, the equation becomes x(120 - x^2), which simplifies to -x^3 + 120x. We can find x by setting the derivative equal to zero, resulting in x = 10. Therefore, the two numbers that maximize the product are 10 and 110, with a product of 12100.
What are the 2 numbers whose product is one called?
Numbers whose product is one is called multiplicative inverses.
Reasons why square numbers are said to be composite numbers?
Prove the opposite.Assume that a square number is prime.A square number is one that is a product of a number multiplied by itselfA prime number is one that has no factors other than itself and 1.For a prime number to be square, the only choice is for it to be 1*1=1Since 1 is not a prime number, there is a contradiction, and the original premise is false.Therefore, all square numbers must be composite.â–
When the square root of one number is multiplied by the square root of a second number the product is the square root of 36 one of the numbers is not 1?
If the two numbers are a and b, then: √a √b = √(ab) = √36 → ab = 36 So any two [positive] numbers whose product is 36 will be a solution, except the pair 1 and 36 as that has been specifically excluded; thus possible solutions are: √4 x √9, √2 x √18, √(1/2) x √72, √(1/4) x √144, etc. (The first one being the only solution where the square roots are whole numbers.)
If the product of two numbers is even then the two numbers must be even right?
Not necessarily, but at least ''one'' of them must be even, unless the two numbers are both the (irrational) square root of the same even number.
What do you call two numbers and their product is one?
The numbers are reciprocals of one another.
What numbers can be made into only one rectangle?
A number can be made into only one rectangle if it is a square number. A square number is a number that can be represented as the product of an integer with itself, such as 1, 4, 9, 16, and so on. These numbers have only one unique way of arranging their factors to form a rectangle, as the sides will be equal in length.
When the product of two numbers is one what are the numbers called?
1
What are two consecutive odd numbers that have a product of 143?
You should be able to find this out quickly with trial and error. Or One more than the product will be the square of the even number between the two odds.
