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3 years ago

PLZ HELP ASAP Find the absolute value of |3x + 7| = 11

Mathematics

1 answer:

tia_tia [17]3 years ago

6 0

Answer:

2 answers, x=-6 and x=1.33

Step-by-step explanation:

When you have abosulte vaule, it makes it positive.

So, what negative number times 3 plus 7 is -11? -6. But then Absolute value makes it positive

It also is 1.33, because 1.33 times 3 plus 7 is 11.

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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

In Erin's career on the basketball team, she made 7 out of every 10 free throws Last season, she

Crazy boy [7]

Answer: 42

For this situation we will use a ratio to show how many free throws Erin will make. Using the ratio 7:10 represents that Erin will make 7 out of every 10 free throws. You want to know how many free throws she will make if she attempts 60 free throws.

Using ratios we will be able to find how many free throws she will make if she attempts 60.

7:10

14:20

21:30

28:40

35:50

42:60

Basically we kept multiply the right side of the ratio which is 10 by 2 until we were at 60 free throws.

Erin will make 42 free throws if she attempts 60 free throws.

6 0

4 years ago

Circle the reason for each of the following manipulations used to simplify the product (8x^2) (3x^7) ?

ipn [44]

Answer:

Running Home and the impact of point of view on events in the poem, “The Sailor.” Use specific examples from BOTH texts to support your answer.

CAN YOU TURN THIS PROMPT INTO A HOW OR WHY QUESTION??

_________________________________________________________

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

in the balcony of a theatre there are 420 seats. the number of seats in each row is 14 more than the number of rows. find the nu

ki77a [65]

420 divided by 14 = 30

There are 30 rows

7 0

3 years ago

15 percent converted to a simply fractin work it a out if your gonna answer

Elza [17]

All percents are out of 100 so start with 15/100 and then simplify

3/20

5 0

4 years ago