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:
x=16
Step-by-step explanation:
multiply both sides of the equation by 2
multiply the number
reduce the number
(i) The product of the two expressions is equal to the product of their factors. (ii) The product of the two expressions is equal to the product of their H.C.F. and L.C.M. 2.
Answer:
The y-axis stays the same
Step-by-step explanation:
:)
Answer: Area (upper bound) = 4527.7056 cm²
Perimeter (lower bound) = 278 cm
<u>Step-by-step explanation:</u>
The length and width of the rectangle have been ROUNDED to the nearest tenth. Let's calculate what their actual measurements could be:
LENGTH: rounded to 87.3, actual is between 87.25 and 87.34
<em>87.25 is the lowest number it could be that would round it UP to 87.3</em>
<em>87.34 is the highest number it could be that would round DOWN to 87.3</em>
WIDTH: rounded to 51.8, actual is between 51.75 and 51.84
<em>51.75 is the lowest number it could be that would round it UP to 51.8</em>
<em>51.84 is the highest number it could be that would round DOWN to 51.8</em>
To find the Area of the upper bound, multiply the highest possible length and the highest possible width:
A = 87.34 × 51.84 = 4527.7056
To find the Perimeter of the lower bound, calculate the perimeter using the lowest possible length and the lowest possible width:
P = 2(87.25 + 51.75) = 278
