I really need help with number 1

Mathematics

1 answer:

Sedaia [141]3 years ago

6 0

3/4 / 2/1
Keep, Change, Flip
3/4 * 1/2 = 3/8

5/4 / 2/1
Keep, Change, Flip

5/4 * 1/2 = 5/8

Answer: 3/8 and 5/8

You might be interested in

A random sample of 41 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $19.55 per car. The p

Rashid [163]

Answer:

$19.55\pm2.145$

Step-by-step explanation:

We use the equation $\bar x\pm z^*\sigma/\sqrt n$ , where $\bar x=19.55$ , $\sigma=6.33$ , $n=41$ , and $z^*=2.17$ . We obtain $z^*$ from the z-score of a 0.97 confidence level.

8 0

2 years ago

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

Help please!!!!<br> Simplify the following <br> Sqrt 100 x ^13

Ket [755]

Answer:

The answer is 10x^6 * sqrt x

Step-by-step explanation:

Hope it works

3 0

3 years ago

A cube is cut into two pieces by a single slice that passes through the points A, B, and C.

masha68 [24]