9514 1404 393
Answer:
split the number into equal pieces
Step-by-step explanation:
Assuming "splitting any number" means identifying parts that have the number as their sum, the maximum product of the parts will be found where the parts all have equal values.
We have to assume that the number being split is positive and all of the parts are positive.
<h3>2 parts</h3>
If we divide number n into parts x and (n -x), their product is the quadratic function x(n -x). The graph of this function opens downward and has zeros at x=0 and x=n. The vertex (maximum product) is halfway between the zeros, at x = (0 + n)/2 = n/2.
<h3>3 parts</h3>
Similarly, we can look at how to divide a (positive) number into 3 parts that have the largest product. Let's assume that one part is x. Then the other two parts will have a maximum product when they are equal. Their values will be (n-x)/2, and their product will be ((n -x)/2)^2. Then the product of the three numbers is ...
p = x(x^2 -2nx +n^2)/4 = (x^3 -2nx^2 +xn^2)/4
This will be maximized where its derivative is zero:
p' = (1/4)(3x^2 -4nx +n^2) = 0
(3x -n)(x -n) = 0 . . . . . . . . . . . . . factor
x = n/3 or n
We know that x=n will give a minimum product (0), so the maximum product is obtained when x = n/3.
<h3>more parts</h3>
A similar development can prove by induction that the parts must all be equal.
Answer: $550.00
Step-by-step explanation: Equation: I = Prt
<u>Calculation:</u>
First, converting R percent to r a decimal
r = R/100 = 2%/100 = 0.02 per year,
then, solving our equation
I = 5500 × 0.02 × 5 = 550
I = $ 550.00
The simple interest accumulated
on a principal of $ 5,500.00
at a rate of 2% per year
for 5 years is $ 550.00.
Hope this helped! ;)
Your goal is to isolate the x variable, so all you have to do here is subtract 6 on both sides.
Your final answer is x ≤ 2.
Hope this helps a lot! :)
To find the average of an amount of numbers, we simply add them up and divide them by the amount of numbers we have. For example, if we have 1,2, and 3 as our numbers, we can see that we have three numbers. Next, we add them up to get 1+2+3=6. Lastly, we divide 6 by the amount of numbers we have (3) to get 6/3=2 as our average. Applying that here, we see that there are four numbers. Next, we add them up using a calculator to get 5,678.54+3,665.77+4,231.98+4,768.99 =18345.28 . Finally, we divide that number by the amount of numbers we have (using a calculator) to get 18345.28/4=4,586.32, making B your answer.
Feel free to ask further questions, and Happy Halloween!
