in general, what does the graph of an equation of the form y=a, where a is any real number, look like?

Mathematics

1 answer:

xeze [42]2 years ago

7 0

Answer:

It will look like a horizontal line. It would go through the y axis is a straight line through a.

Step-by-step explanation:

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Find cos θ given that cos 2θ = 5/6 and 0 ≤ θ < π/2. Give an exact answer

trasher [3.6K]

$\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
1-2sin^2(\theta)\\
\boxed{2cos^2(\theta)-1}
\end{cases}
\\ \quad \\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-------------------------------\\\\
$

$\bf cos(2\theta)=\cfrac{5}{6}\implies 2cos^2(\theta)-1=\cfrac{5}{6}\implies 2cos^2(\theta)=\cfrac{5}{6}+1
\\\\\\
2cos^2(\theta)=\cfrac{11}{6}\implies cos^2(\theta)=\cfrac{11}{12}\implies cos(\theta)=\pm\sqrt{\cfrac{11}{12}}$

now, bear in mind, the square root gives us +/- versions, so, which is it? well, we know the angle is in the range of "<span>0 ≤ θ < π/2", that simply means the 1st quadrant, so, we'll use the positive one then

</span> $\bf cos(\theta)=\cfrac{\sqrt{11}}{\sqrt{12}}\implies cos(\theta)=\cfrac{\sqrt{11}}{2\sqrt{3}}
\\\\\\
\textit{now, let's rationalize the denominator}
\\\\\\
\cfrac{\sqrt{11}}{2\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{\sqrt{11}\cdot \sqrt{3}}{2\sqrt{3^2}}\implies \cfrac{\sqrt{11\cdot 33}}{2\cdot 3}\implies \boxed{\cfrac{\sqrt{33}}{6}}$ <span>
</span>

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Answer:

x= (4,-7)

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Step-by-step explanation:

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A recipe for banana pudding calls for 2 cups of flour and 1 1/2 cups of butter. If 5 cups of flour were used, how many cups of b

8090 [49]

Answer:

You would need a total of 3 3/4 cups. First double the amount of butter= 3 cups, then half 1 1/2 cups for the last cup of flour which would be 3/4. Add them together, it would equal 3 3/4 cups.

Step-by-step explanation:

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Svetach [21]

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What three ratios are equal to 10:5?

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