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3 years ago

If cos(x)cos(π/7)+sin(x)sin(π/7)= - (√2)/2, then x can equal:

1 answer:

8 0

$\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\$

$\bf cos(x)cos\left( \cfrac{\pi }{7} \right)+sin(x)sin\left( \cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2}\implies cos\left( x-\cfrac{\pi }{7} \right)=-\cfrac{\sqrt{2}}{2} \\\\\\ x-\cfrac{\pi }{7}=cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies x-\cfrac{\pi }{7}= \begin{cases} \frac{3\pi }{4}\\\\ \frac{5\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill$

$\bf x-\cfrac{\pi }{7}=\cfrac{3\pi }{4}\implies x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{3\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n} \\\\[-0.35em] ~\dotfill\\\\ x-\cfrac{\pi }{7}=\cfrac{5\pi }{4}\implies x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~\hfill \stackrel{n ~\in~ \mathbb{Z}}{x=\cfrac{5\pi }{4}+\cfrac{\pi }{7}~~~~+2\pi n}$

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2 years ago

When a person is breathing normally the amount of air in their lawns varies sinusoidally. When full Karen’s lungs hold 2.8 L of

makkiz [27]

Answer:

$A(t) = 2.2\sin \frac{(t - 2)\pi }{6} + 0.6$

Step-by-step explanation:

Let the function of quantity in the lung of air be A(t)

So $A(t) \alpha \sin (\frac{t - \alpha }{k} )$

so, A(t) = Amax sin t + b

A(t) = 2.8t⇒ max

A(t) = 0.6t ⇒ min

max value of A(t) occur when sin(t) = 1

and min value of A(t) = 0

So b = 0.6

and A(max) = 2.2

$A(t) = 2.2\sin \frac{(t)}{k} + 0.6$

at t = 2 sec volume of a is 0.6

So function reduce to

$A(t) = 2.2\sin \frac{(t - 2)}{k} + 0.6$

and t = 5 max value of volume is represent

so,

$\sin \frac{t - \alpha }{k} = 1$

$\frac{t - 2}{k} = \frac{\pi }{2}$ when t = 5

$\frac{6}{\pi } = k$

so the equation becomes

$A(t) = 2.2\sin \frac{(t - 2)\pi }{6} + 0.6$

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3 years ago

The team mascot shoots a rolled T-shirt from a special T-shirt cannon to a section of people in the stands at a basketball game.

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For this parabola we have:
f ( 0 ) = 8
and : f ( 1 ) = 24
In the first equation ( A) :
f ( 0 ) = - 16 * ( 0 - 1 )² + 24 = - 16 * 1 + 24 = 8 ( correct )
f ( 1 ) = - 16 * ( 1 - 1 )² + 24 = 24 ( correct )
For B:
f ( 0 ) = - 16 * ( 0 + 1 )² + 24 = - 16 + 24 = 8 ( correct )
f ( 1 ) = - 16 * ( 1 + 1 )² + 24 = - 16 * 4 + 24 = - 64 + 24 = 40 ( false )
For C:
f ( 0 ) = - 16 * ( 0 - 1 )² - 24 = - 16 - 24 = - 40 ( false )
f ( 1 ) = - 16 * ( 1 - 1 )² - 24 = - 24 ( false )
For D:
f ( 0 ) = - 16 * ( 0 + 1 )² - 24 = - 16 - 24 = - 40 ( false )
f ( 1 ) = - 16 * ( 1 - 1 )² - 24 = - 24 ( false )
Answer:
A ) f ( t ) = - 16 * ( t - 1 )² + 24

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