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4 years ago

Find the critical numbers sin^2x+cosx 0 < x< 2pi

1 answer:

5 0

$\bf sin^2(x)+cos(x)\iff [sin(x)]^2+cos(x)\\\\
-----------------------------\\\\
\cfrac{dy}{dx}=2sin(x)cos(x)-sin(x)\implies 0=2sin(x)cos(x)-sin(x)
\\\\\\
0=sin(x)[2cos(x)-1]\implies 
\begin{cases}
0=sin(x)\\
sin^{-1}(0)=\measuredangle x\\
\pi \\
----------\\
0=2cos(x)-1\\\\ \frac{1}{2}=cos(x)\\\\ cos^{-1}\left( \frac{1}{2} \right)=\measuredangle x\\\\ \frac{\pi }{3},\frac{5\pi }{3}
\end{cases}$

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Given:

A figure of a triangle.

To find:

The measure of angle A.

Solution:

Label the points in the figure as shown below.

In the below figure,

$\angle ACB\cong \angle DCE$ (Vertically opposite angles)

$m\angle ACB=m\angle DCE$ (Congregant angles)

$m\angle ACB=8x+4$

Using exterior angle theorem in triangle ABC, we get

$m\angle A+m\angle C=\text{Exterior }m\angle B$

$m\angle BAC+m\angle ACB=130^\circ$

$(3x-6)+(8x+4)=130^\circ$

$11x-2=130^\circ$

Isolate the variable term x.

$11x=130^\circ+2$

$11x=132^\circ$

$x=\dfrac{132^\circ}{11}$

$x=12^\circ$

Now, the measure of angle A is:

$m\angle A=3x-6$

$m\angle A=3(12^\circ)-6$

$m\angle A=36^\circ-6$

$m\angle A=30^\circ$

Therefore, the correct option is B.

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3 years ago

Elise built a large rectangular vegetable garden that is 9 meters long and has an area of 72 square meters.

olya-2409 [2.1K]

Answer:

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Step-by-step explanation:

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

Solve the equation by completing the square. Round to the nearest hundredth if necessary. X^2 + 5x-10=0

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$(*)\\(a+b)^2=a^2+2ab+b^2$

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