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3 years ago

5

X+y= 2

2 answers:

Free_Kalibri [48]3 years ago

8 0

11 is the answer to the question

bija089 [108]3 years ago

4 0

Answer:

11

Step-by-step explanation:

11

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Determine whether the following series converge or diverge

Mars2501 [29]

An alternating series $\sum\limits_n(-1)^na_n$ converges if $|(-1)^na_n|=|a_n|$ is monotonic and $a_n\to0$ as $n\to\infty$ . Here $a_n=\dfrac1{\ln(n+1)}$ .

Let $f(x)=\ln(x+1)$ . Then $f'(x)=\dfrac1{x+1}$ , which is positive for all $x>-1$ , so $\ln(x+1)$ is monotonically increasing for $x>-1$ . This would mean $\dfrac1{\ln(x+1)}$ must be a monotonically decreasing sequence over the same interval, and so must $a_n$ .

Because $a_n$ is monotonically increasing, but will still always be positive, it follows that $a_n\to0$ as $n\to\infty$ .

So, $\sum\limits_n(-1)^na_n$ converges.

5 0

3 years ago

Can you please help me with this question please help and i will give you a Brainiest

patriot [66]

Answer:

Cans for food drive

Step-by-step explanation:

6 0

3 years ago

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Find gradient <br><br>xe^y + 4 ln y = x² at (1, 1)

cricket20 [7]

$xe^y+4\ln y=x^2$

Differentiate both sides with respect to <em>x</em>, assuming <em>y</em> = <em>y</em>(<em>x</em>).

$\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}$

$\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x$

$\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

$e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

Solve for d<em>y</em>/d<em>x</em> :

$e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x$

$\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}$

If <em>y</em> ≠ 0, we can write

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}$

At the point (1, 1), the derivative is

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}$

4 0

3 years ago

Choose the answer that validates that the rate of change is constant by showing that the ratios of the two quantities are propor

docker41 [41]

Given:

The table of values is

Number of Students : 7 14 21 28

Number of Textbooks : 35 70 105 140

To find:

The rate of change and showing that the ratios of the two quantities are proportional and equivalent to the unit rate.

Solution:

The ratio of number of textbooks to number of students are

$\dfrac{35}{7}=5$

$\dfrac{70}{14}=5$

$\dfrac{105}{21}=5$

$\dfrac{140}{28}=5$

All the ratios of the two quantities are proportional and equivalent to the unit rate.

Let y be the number of textbooks and x be the number of students, then

$\dfrac{y}{x}=k$

Here, k=5.

$\dfrac{y}{x}=5$

$y=5x$

Hence the rate of change is constant that is 5.

8 0

3 years ago

The points where a graph crosses the x- and y-axis are called the _____.

Marina CMI [18]

I think it's called a coordinate plane

Sorry if I'm wrong

6 0

3 years ago

Read 2 more answers