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:
The attached file contains the solution to the question
Answer:
Monique made an error when writing the factored expression.
Correct factored
expression=4x(1+4y)
Step-by-step explanation:
factoring the expression 4 x + 16 x y.
Factors of 4x: 1, 2, 4, x
Factors of 16xy: 1, 2, 4, 8, 16, x, y
GCF: 4x
Factored expression: 4 x (0 + 4 y)
Monique made an error when writing the factored expression.
The correct factored expression should be:
4x+16xy
=4x(1+4y)
Contrary to 4x(0+4y)
Correct factored
expression=4x(1+4y)
Answer:
Step-by-step explanation:
We have to find the quotient of the following division, 
.
Now,
= ![- \frac{3}{4} p^{[- 4 - (- 12)]} q^{[-6 - (- 3)]}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B3%7D%7B4%7D%20p%5E%7B%5B-%204%20-%20%28-%2012%29%5D%7D%20q%5E%7B%5B-6%20-%20%28-%203%29%5D%7D)
{Since all the terms in the expression are in product form, so we can treat them separately}
{Since we know the property of exponent as 
}
= 
= (Answer)
{Since we know, 
}
Answer: 37 you just add the two in that case
