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3 years ago

7

Altogether Central High School's bands have 40 trumpets and 35 tubas. Carlee says the ratio of trumpets to tubas is 40:35. Danny

disagrees and says the ratio is 8:7.
Actually, they are both correct. Explain why these are equivalent ratios.

1 answer:

Evgen [1.6K]3 years ago

4 0

Answer:

because if in 40:35 you divide 40 and 35 by 5 it is equal to 8:7

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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)}\\\\\\
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—————

• Method II:

You can also treat y as a composite function:

$\left\{\!
\begin{array}{l}
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and then, differentiate y by applying the chain rule:

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\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>

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