Let the number be n.
Then:
n^2 + (1/n)^2 = 82/9; find n. Find the LCD; it is 9n^2.
Mult all 3 terms by 9n^2:
82*9n^2
9n^4 + 9 = (82/9)(9n^2) => 9n^4 + 9 = ------------
9
Then 9n^4 - 82n^2 + 9 = 0
I used my graphing calculator to find that n = 3.
Let's check: is 3^2 + (1/3)^2 = 82/9?
Is 9 + 1/9 = 82/9?
Is 81 + 1 = 82? YES. So, n=3 is a solution.
We write the expression in its simplest form and we are left with.
y²√3 + y - 6
Before proceeding let's define an algebraic expression.
<h3>Algebraic expression</h3>
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
The first thing we will do is to write the expression:
(√y-√3)(√y+2√3)
Then we perform the multiplication, with the distributive property, which gives as a result
(y + 2√3y - √3y - 6)
y²√3 + y - 6
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X=12
. . . . . . . . . . . . . . . . . . . .
A pair of the opposite sides of a regular hexagon has equal length,
<h3>What is a regular hexagon?</h3>
A regular hexagon is defined as a closed shape consisting of six equal sides and six equal angles. The sum of the measure of interior angles of a regular hexagon is 720 degrees.
The total of the interior angles is 180°(n -2), where n is the number of sides of the convex polygon. Thus for a regular polygon of n sides, the interior angles are each.
(180°)(n -2)/n = 180° -(360°/n)
Let us assume the each angle of the hexagon = m
m + m + m + m + m + m = 720°
or, 6 m = 720°
or, m = 720° / 6 = 120°
Hence Each interior angle of the Regular Hexagon is 120°
A pair of the opposite sides of a regular hexagon has equal length,
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-0.25. You basically divide 1 by 4 and you will get the decimal form. Also you add the negative
