Attached is a screenshot of another problem I am having issues with. please please please help me

Mathematics

1 answer:

anyanavicka [17]3 years ago

4 0

$\bf cos(\alpha+\beta)cos(\alpha-\beta)\\\\
-----------------------------\\\\
\textit{using the sum identities}\\\\\

\begin{array}{ccccccll}
[cos(\alpha)cos(\beta)&-&sin(\alpha)sin(\beta)]&[cos(\alpha)cos(\beta)&+&sin(\alpha)sin(\beta)]\\
a&-&b&a&+&b
\end{array}\\\\
\textit{notice above, is just a difference of squares, thus}
\\\\\\\
[cos(\alpha)cos(\beta)]^2-[sin(\alpha)sin(\beta)]^2\\\\
\textit{now let us distribute the exponents}\\\\$

$\bf cos^2(\alpha)cos^2(\beta)-sin^2(\alpha)sin^2(\beta)\\\\
-----------------------------\\\\
\textit{now, let us use the pythagorean identity of }\\\\
sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\
-----------------------------\\\\\
[ 1-sin^2(\alpha)][ 1-sin^2(\beta)]-sin^2(\alpha)sin^2(\beta)
\\\\\\\
1-sin^2(\beta)-sin^2(\alpha)\underline{+sin^2(\alpha)sin^2(\beta)-sin^2(\alpha)sin^2(\beta)}
\\\\\\
\underline{1-sin^2(\beta)}-sin^2(\alpha)\implies cos^2(\beta)-sin^2(\alpha)$

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Abraham has visited 10 countries already. He has a goal of visiting at least 50 countries. He plans to achieve this goal by visi

olasank [31]

Given :

Abraham has visited 10 countries already. He has a goal of visiting at least 50 countries.

He plans to achieve this goal by visiting 5 new countries per year (y) for the next several years.

To Find :

Which inequality and solution shows the amount of years that it will take for Abraham to meet his goal.

Solution :

Let, after x years Abraham visited y countries.

It is mathematically given as :

$10 + 5x=y$