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3 years ago

At what point on the curve y=x+2cos x is the tangent horizontal in the interval [-2pi, 2pi]

1 answer:

8 0

$\bf y=x+2cos(x)\qquad \qquad [-2\pi ,2\pi ]\\\\
-----------------------------\\\\
\cfrac{dy}{dx}=1-2sin(x)\implies 0=1-2sin(x)\implies sin(x)=\cfrac{1}{2}
\\\\\\
\measuredangle x=sin^{-1}\left( \frac{1}{2} \right)\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}\\\\
\frac{5\pi }{6}
\end{cases}$

only in the 1st and 2nd quadrants, where sine is positive

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timofeeve [1]

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3 years ago

Consider a population whose growth over a given time period can be described by the exponential model: dN/dt = rN. Select the co

pantera1 [17]

Answer:

b and c

Step-by-step explanation:

We are given that a population whose growth over a given time period can be described by the exponential model

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After integrating

We get ln N=rt +C

Where C is integration constant

When t=0 then N= $N_0$

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Substitute the value of C then we get

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When r= 0

Then we get

$N=N_0e^{0}$

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3 years ago

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OverLord2011 [107]

Answer:

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A perfect square would be:

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But we need -3r^2 so we add - r^2 at the end:

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(r^2 - 1)^2 - r^2

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11 months ago