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3 years ago

Which statement is true regarding the angles in the figure below?

Mathematics

2 answers:

Nesterboy [21]3 years ago

8 0

An exterior angle is an angle supplementary to one of the interior angles.

In other words, an exterior angle is the angle between one of the sides, and the extension of an adjacent side.

In the given diagram, the angle D is measured from one of the sides, but not to the extension of an adjacent side.

Therefore angle D is not an exterior angle.

Option D is the correct one!

S_A_V [24]3 years ago

3 0

Answer:

Angle D is not an exterior angle

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How to find the derivative of cos^2x? i seem to be confused.

slamgirl [31]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2927231

————————

You can actually use either the product rule or the chain rule for this one. Observe:

• Method I:

y = cos² x

y = cos x · cos x

Differentiate it by applying the product rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}$

The derivative of cos x is – sin x. So you have

$\mathsf{\dfrac{dy}{dx}=(-sin\,x)\cdot cos\,x+cos\,x\cdot (-sin\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=-sin\,x\cdot cos\,x-cos\,x\cdot sin\,x}$

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

—————

• Method II:

You can also treat y as a composite function:

$\left\{\!
\begin{array}{l}
\mathsf{y=u^2}\\\\
\mathsf{u=cos\,x}
\end{array}
\right.$

and then, differentiate y by applying the chain rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(u^2)\cdot \dfrac{d}{dx}(cos\,x)}$

For that first derivative with respect to u, just use the power rule, then you have

$\mathsf{\dfrac{dy}{dx}=2u^{2-1}\cdot \dfrac{d}{dx}(cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2u\cdot (-sin\,x)\qquad\quad (but~~u=cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2\,cos\,x\cdot (-sin\,x)}$

and then you get the same answer:

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>

3 0

3 years ago

PLEASE DO NOT ANSWER THIS EMPTY OR ADD A LINK OR SAY "Answer is in here!" I WILL REPORT YOU IF YOU DO. I DO NOT TAKE FILES PLEAS

Goryan [66]

Answer:

M=2

Step-by-step explanation:

rise over run

you rise 2 and go over 1

2 over 1 is just 2.

3 0

3 years ago

Read 2 more answers

The Gaineys and the Arnolds are saving money for a trip to Utah to go snowboarding. The Arnolds are going to save a nickel on th

natali 33 [55]

Answer: see Explanation

Step-by-step explanation:

THE GAINEY'S:

Recursive Formula :

A1 = $10

An = An-1 + $10

A2 = $10 + $10 = $20

Where n = day of the month

Explicit formula :

y = a + b(c - 1)

WHERE:

y = final amount

initial amount = a

Increment on initial amount = b

Day of the month = c

THE ARNOLD'S :

Recursive formula:

First day of the month (A1) = $10

An = 2(An-1)

A2 = 2(A1) = 2(10) = $20

A3 = 2(A2) = 2(20) =$40

Explicit formula:

y = a(b)^c

Where :

y = final amount

initial amount = a

Increment on initial amount = b

Day of the month = c

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3 years ago

3(X + 3) 3/4 = 81 <br> what is the answer

Genrish500 [490]

Answer:

the correct answer would be 33

Step-by-step explanation:

hope this helps :)

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2 years ago

In a distribution system that's operating at 4.160 kV, what is the voltage level in volts? A. 4.160 volts B. 4,160 volts C. 0.00

Romashka-Z-Leto [24]

The answer to this question is a 4160 volta

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