The apothem is the distance from which the altitudes of the triangle to one of its sides. It can be calculated through the equation below,
tan 30° = apothem / 0.5(length of side)
Substituting the known values,
tan 30° = 5 / 0.5x
The value of x from the equation above is 17.32. Multiplying this value by 3 (because a triangle has 3 sides), we get an answer of 51.96 cm or approximately equal to 52. Thus, the answer is letter B.

5 0

3 years ago

P(x)= x^5-4x^4+3x^3+2x-6 <br> Use Descartes rule of signs to analyze the zeros

maxonik [38]

$\bf \begin{array}{cccccccccccllll}
P(x)= x^5&-&4x^4&+&3x^3&+&2x&-&6\\
&yes&&yes&&\textit{no}&&yes
\\\\\\
P(-x)= -x^5&-&4x^4&-&3x^3&-&2x&-&6\\
&\textit{no}&&\textit{no}&&\textit{no}&&\textit{no}
\end{array}$

notice where how many "yes" sign change happen in the positive "x"
and the on the negative "-x"

for the P(x) is 3 changes, thus
so is either 3 real positive ones, or 3-2 = 1 real positive one

P(-x) gives no sign changes, so there are 0 negative ones

the polynomial has a degree of 5, thus 5 roots
if it has 3 real positive ones, then it has 2 complex ones
the complex ones pick up the slack per se

if it has 1 real positive one, then it has 4 complex ones

bear in mind complex ones always come in pairs

8 0

3 years ago