What percent of 134 is 66? (To the nearest tenth of a percen t)

Mathematics

1 answer:

dezoksy [38]3 years ago

3 0

Answer: 49.25

Step-by-step explanation:

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Find exact value of cos(2 tan^-1(12/5))

SCORPION-xisa [38]

$\bf cos\left[2\ tan^{-1}\left( \frac{12}{5} \right) \right]
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\textit{let's say, hmm }tan^{-1}\left( \frac{12}{5}\right)=\theta\textit{ that simply means}
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cos\left[2\ tan^{-1}\left( \frac{12}{5} \right) \right]\iff cos(2\theta)\implies 2cos^2(\theta)-1\leftarrow 
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using\\
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identities
\end{array}$

$\bf \textit{so hmm what is the }cos(\theta)?\quad cos(\theta)=\cfrac{adjacent}{hypotenuse}
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\textit{so, let's use the pythagorean theorem, to get the hypotenuse}
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tan^{-1}\left( \frac{12}{5}\right)=\theta\implies tan(\theta)=\cfrac{12}{5}\cfrac{\leftarrow opposite=b}{\leftarrow adjacent=a}
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c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\implies c=\sqrt{5^2+12^2}\implies c=\sqrt{169}
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c=13$

$\bf 2cos^2(\theta)-1\iff 2\left[ cos(\theta) \right]^2-1\implies 2\left[ \cfrac{5}{13} \right]^2-1
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2\cdot \cfrac{25}{169}-1\implies \cfrac{50}{169}-1\implies -\cfrac{119}{169}$

5 0

3 years ago

the gray whale can spend up to 30 minutes underwater. How many times will the whale need to come up for air during a 6hr period

Vinvika [58]

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Hello!

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❖ The gray whale will need to come up 12 times during the 6 hr period.

Convert 6 hrs to mins:

1 hr = 60 mins

60 x 6 = 360 mins

Divide by 30 to see how many times the whale will need to come up: