What is the Greatest Value of an Expression with Given Numbers and Equation?

  • MHB
  • Thread starter anemone
  • Start date
In summary, an expression is a mathematical statement that represents a value or relationship between quantities using numbers, variables, and operations. The given numbers in an expression are the numerical values used in the equation, and the equation is the mathematical relationship between the given numbers and operations used to manipulate them. To find the greatest value of an expression, the given numbers are plugged into the equation and solved using order of operations. This value can change if the numbers or equation are altered.
  • #1
anemone
Gold Member
MHB
POTW Director
3,883
115
Here is this week's POTW:

-----

The numbers $x_1,\,x_2,\,\cdots,\,x_{1991}$ satisfy the equation $|x_1-x_2|+|x_2-x_3|+\cdots+|x_{1990}-x_{1991}|=1991$.

What is the greatest possible value of the expression $|y_1-y_2|+|y_2-y_3|+\cdots+|y_{1990}-y_{1991}|$, where $y_k=\dfrac{1}{k}(x_1+x_2+\cdots+x_k)$?

-----

 
Physics news on Phys.org
  • #2
As usual, I will give the community another week's time to attempt at last week's POTW. And I am looking forward to receiving submissions from the members!
 

1. What is the process for finding the greatest value of an expression with given numbers and equation?

The process for finding the greatest value of an expression involves substituting the given numbers into the equation and simplifying the expression. Then, you can use mathematical operations such as addition, subtraction, multiplication, and division to find the maximum value.

2. How can I identify the greatest value when there are multiple variables in the expression?

To identify the greatest value when there are multiple variables, you can use algebraic techniques such as factoring, completing the square, or using the quadratic formula. These methods will help you simplify the expression and find the maximum value.

3. Is there a specific order in which I should solve the expression to find the greatest value?

Yes, there is a specific order in which you should solve the expression to find the greatest value. This order is known as the order of operations, which states that you should solve operations in parentheses first, followed by exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

4. Can I use a calculator to find the greatest value of an expression?

Yes, you can use a calculator to find the greatest value of an expression. However, it is important to make sure you are using the correct order of operations and inputting the numbers and equation correctly to get an accurate result.

5. What is the significance of finding the greatest value of an expression in scientific research?

Finding the greatest value of an expression is important in scientific research because it allows us to identify the maximum potential or outcome of a given situation. This can help researchers make informed decisions and predictions based on the data and equations at hand.

Similar threads

MHB Maximize (x1+x2)(x1+x3)x4 for Quartic Equation with Real Roots in [1/2,2]
    • Math POTW for Secondary and High School Students
Replies
2
Views
937
B General explicit solution to polynomial interpolation
    • General Math
Replies
3
Views
738
MHB The value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$ is 1234.
    • Math POTW for Secondary and High School Students
Replies
1
Views
896
A Find Noether Normalization
    • Linear and Abstract Algebra
Replies
14
Views
1K
Mass on a wedge, both can move
    • Advanced Physics Homework Help
Replies
5
Views
1K
MHB Summation Challenge: Evaluate $\sum_{k=1}^{2014}\frac{1}{1-x_k}$
    • General Math
Replies
2
Views
828
I FEM 2D Node Equations: Setting Up & Examples
    • Differential Equations
Replies
9
Views
2K
Sum of Infinite Series: Finding the Value of S
    • Precalculus Mathematics Homework Help
Replies
10
Views
2K
MHB Minimum Value of Sum of Squares: POTW #235 (Sep 27, 2016)
    • Math POTW for Secondary and High School Students
Replies
1
Views
1K
B Are continuous functions on sequentially compact sets u-continuous?
    • Calculus
Replies
18
Views
2K

Recent Insights

Back
Top