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:
both statements are fine
Step-by-step explanation:
To find the price of a product after decreasing it, they can be done in the two ways that the statement tells us,
First, calculate that% that was decreased and then subtract it from the original price or simply multiply that original price by the percentage in which the new price would remain.
For example:
let "x" be the original price
in the first case it would be:
0.2 * x and then subtract from x, i.e .:
x - 0.2 * x
in the second case it is:
1 - 0.2 = 0.8
that is, the new price would be 0.8 * x
Answer:
Step-by-step explanation:
Given
Required
Determine the volume of air
Density is calculated using:
Substitute values for Density and Mass
Convert lb to grams
Solve for Volume
Convert mL to L
Represent using scientific notation
Approximate
To write 32,005,008 in expanded form, you write it out like this: <span>32,005,008 = 30,000,000 + 2,000,000 + 5,000 + 8.
I know this because I learned it in 3rd grade at school.
Hope I helped!
- Debbie
</span>
Answer:
Step-by-step explanation:
Integrating each term with respect to x, we get:
x^3 x^2
f(x) = 9--------- + 4------- - 4x + C
3 2
We are told that if x = 0, f(x) = -7, and so C must equal - 7.
The solution is
x^3 x^2
f(x) = 9--------- + 4------- - 4x - 7, or f(x) = 3x^3 + 2x^2 - 4x - 7
3 2
