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.
Answers:
tan(A) = 8/15
sin(A) = 8/17
cos(A) = 15/17
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Explanation:
The tangent ratio involves the opposite over adjacent. With respect to angle A, the opposite side is 8 units long as this side is as far as possible away from angle A. In contrast, the adjacent side is 15 units long because this leg is closest possible and the two are right next to one another.
Therefore,
tan(angle) = opposite/adjacent
tan(A) = BC/AC
tan(A) = 8/15
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As for the other trig ratios, they are:
sin(angle) = opposite/hypotenuse
cos(angle) = adjacent/hypotenuse
which explains why sin(A) and cos(A) are 8/17 and 15/17 respectively.
Answer:
I think standard form would be best because it is simplest.
Step-by-step explanation:
hope this helps
Answer: idk the answer but i can tell u that u are trying to find the value of the symbols and the numbers :)
Step-by-step explanation:
