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3 years ago

Lukas is able to package and ship 416 cards in an 8-hour workday. How many cards can Lukas package a ship 32 hours?

Mathematics

1 answer:

jeka943 years ago

6 0

Answer:

1664 cards

Step-by-step explanation:

416 divided by 8 is 52 and 52 times 32 is 1664.

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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

4 years ago

His triangle has a perimeter of 48 feet. The second side is 5 feet longer than the first side. The third side is 3 feet longer t

kotegsom [21]

Answer:

The length of the second side is 22.5 feet.

Step-by-step explanation:

7 0

3 years ago

A figure is composed of two half-circles.

posledela

Answer:

The answer is C, 220 units.

3 0

3 years ago

Chris wants to order DVDs over the internet.

Nuetrik [128]

Step-by-step explanation:

14d +9 <100

14d represents cost for dvds. 9 is the flat rate shipping. all must be less than 100

6 0

4 years ago

Read 2 more answers

Which term best describes lines that meet at right angles ?

Sholpan [36]

Answer:

Perpendicular

Step-by-step explanation:

Perpendicular lines meet at a 90 degree angle.

5 0

3 years ago