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3 years ago

For the function

" align="absmiddle" class="latex-formula">, what are the coordinates of the vertex?
Is it a maximum or minimum point?

Hint: consider using $x=-b/2a$ . Show all work algebraically

SERIOUS ANSWERS ONLY! NO SPAM!

Mathematics

1 answer:

Gre4nikov [31]3 years ago

8 0

$x_0=\dfrac{-b}{2a} =\dfrac{-4}{2\times(-2)}=1\\y_0=-2\times1^2+4\times1+1=-2+4+1=3\\Answer: The\: vertex\: is \:(1;3). It's\:maximum\:point \:because \:a=-2$

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Step-by-step explanation:

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3 years ago

Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

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Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

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8 months ago

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poizon [28]

Answer:

16/49

Step-by-step explanation:

4/7 ÷ 1 3/4

Convert 1 3/4 into an improper fraction

4/7 ÷ 7/4

Find the reciprocal of 7/4 and multiply

4/7 * 4/7

16/49

Hope this helps :)

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2 years ago