9514 1404 393
Answer:
2(x+1)
Step-by-step explanation:
x . . . I think of a number
x +1 . . . add 1
2(x +1) . . . double the result
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:
Q5) 7
Q6) 4
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Step-by-step explanation:
The different is that 21 is going ALL the way down to 21 while 4 is only going to 4..
Intensive properties and extensive properties are types of physical properties of matter. The terms intensive and extensive were first described by physical chemist and physicist Richard C. Tolman in 1917. Here's a look at what intensive and extensive properties are, examples of them, and how to tell them apart.
Intensive Properties
Intensive properties are bulk properties, which means they do not depend on the amount of matter that is present. Examples of intensive properties include:
Boiling point
Density
State of matter
Color
Melting point
Odor
Temperature
Refractive Index
Luster
Hardness
Ductility
Malleability
Intensive properties can be used to help identify a sample because these characteristics do not depend on the amount of sample, nor do they change according to conditions.
Extensive Properties
Extensive properties do depend on the amount of matter that is present. An extensive property is considered additive for subsystems. Examples of extensive properties include:
Volume
Mass
Size
Weight
Length
The ratio between two extensive properties is an intensive property. For example, mass and volume are extensive properties, but their ratio (density) is an intensive property of matter.
While extensive properties are great for describing a sample, they aren't very helpful identifying it because they can change according to sample size or conditions.
Way to Tell Intensive and Extensive Properties Apart
One easy way to tell whether a physical property is intensive or extensive is to take two identical samples of a substance and put them together. If this doubles the property (e.g., twice the mass, twice as long), it's an extensive property. If the property is unchanged by altering the sample size, it's an intensive property.
