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3 years ago

Match each logarithm to its value

Mathematics

1 answer:

valkas [14]3 years ago

7 0

Answer:

Step-by-step explanation:

In the picture ⬆️

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In a certain Algebra 2 class of 30 students, 22 of them play basketball and 18 of them play baseball. There are 3 students who p

PolarNik [594]

Using the rules of probability:

P(A∩B)=P(A)+P(B)−P(A∪B) = 22/30 + 18/30 − 27/30 = 13/30 Play both.

3 0

4 years ago

Cos^-1(cos 43°) PLEASE HELP ME

yulyashka [42]

$\: \: \: \: \:$

$= \cos(1) \cos(43°) \\ \\ in \: \: alternate \: \: form \: \\ \\ = 0.395152$

<h2 />

Step-by-step explanation:

$\cos( - 1) ( \cos(43°))$

simplify the expression usiNg the symmetry of trigonometry

 $= \cos(1) \cos(43°) \\ \\ \\ or \: \: in \: \: alternate \: \: form \\ \\ = 0.395152$ 

<h2>hope it helps</h2>

4 0

3 years ago

Read 2 more answers

What is -22 = -9 +n

earnstyle [38]

Answer:

If you are looking for n then

N = -13

Step-by-step explanation:

-13+-9 is -22

4 0

3 years ago

Read 2 more answers

Can you’ll help me pls

Rasek [7]

Answer:

1. 48 sticks, 49 dots

2. 60 sticks, 61 dots

3. figure 13, 157 dots

Step-by-step explanation:

The pattern increases by 12 sticks each time. The number of dots is equal to the number of lines plus 1. An easy way to figure it out is to multiply the figure number by 12 to find the number of lines and then add one more for the number of dots. To solve 3, divide the number of sticks by 12 to find the figure number, and add one to the number of sticks to get the number of dots.

3 0

3 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: derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus

3 0

4 years ago