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:
4600
Step-by-step explanation:
This is an arithmetic sequence with common difference d between consecutive terms.
d = - 2 - (- 6) = 2 - (- 2) = 6 - 2 = 4
The sum to n terms of an arithmetic sequence is
= 
[ 2a + (n - 1)d ]
where a is the first term
here a = - 6, d= 4 and n = 50, hence
= 
[ (2 × - 6) + (49 × 4) ]
= 25 ( - 12 + 196 )
= 25 × 184
= 4600
Answer:
Sophia now has 39 cents.
Step-by-step explanation:
One quarter = 25 cents
Since Sophia had 64 cents until she spent 25 cents (1 quarter).
So we subtract 25 cents from 64 cents.
Therefore, Sophia now has 39 cents.
I believe the answer to your question is 23
