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3 years ago

Triangle LMN has the vertices shown on the coordinate grid.

Mathematics

1 answer:

Kisachek [45]3 years ago

7 0

9514 1404 393

Answer:

d. √74 units

Step-by-step explanation:

The distance formula is useful for finding the length of a line segment.

d = √((x2 -x1)^2 +(y2 -y1)^2)

Filling in the point coordinates L(-5, -3) and M(0, 4), we find the length of LM to be ...

LM = √((0-(-5))^2 +(4 -(-3))^2) = √(25 +49)

LM = √74 . . . units

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Answer:

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Step-by-step explanation:

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3 years ago

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4 years ago

Given that y = sin(x+y),find the derivative when (x,y)=(π,0)

lisov135 [29]

<h2>Answer:</h2>

Shown in the explanation

<h2>Step-by-step explanation:</h2>

Recall that an implicit function is a relation given by the form:

$R(x_{1},\ldots, x_{n})=0$

Where $R$ is a function of two or more variables. In this case, that function is:

$y = sin(x+y)$

and is implicit because we can define it as:

$y-sin(x+y)=0$ having two variables.

So, let's take the derivative:

$\frac{d}{dx}\left(y\right)=\frac{d}{dx}\left(\sin \left(x+y\right)\right) \\ \\$

Applying chain rule:

$\frac{d}{dx}\left(\sin \left(x+y\right)\right)=\cos \left(x+y\right)\left(1+\frac{d}{dx}\left(y\right)\right)$

But:

$\frac{d}{dx}\left(y\right)=y'$

Therefore:

$y'=\cos \left(x+y\right)\left(1+y'\right)$

Isolating $y'$ :

$\frac{d}{dx}\left(y\right)=y'=\frac{\cos \left(x+y\right)}{1-\cos \left(x+y\right)}$

When $(x,y)=(\pi,0)$ :

$\frac{d}{dx}\left(y\right)|_{(\pi,0)}=\frac{\cos \left(\pi+0\right)}{1-\cos \left(\pi+0\right)} \\ \\ \frac{d}{dx}\left(y\right)|_{(\pi,0)}=\frac{\cos \left(\pi\right)}{1-\cos \left(\pi\right)} \\ \\ \frac{d}{dx}\left(y\right)|_{(\pi,0)}=\frac{-1}{1-(-1)} \\ \\ \boxed{\frac{d}{dx}\left(y\right)|_{(\pi,0)}=-\frac{1}{2}}$

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3 years ago

X= 2/3 y= 1/2 z=4 2/3 work out the value of z+x *y

Blizzard [7]

Answer: 16/9 or 1 7/9

Step-by-step explanation:

plug in the values

4 2/3 + 2/3 * 1/2

add the first two values

4 2/3 + 2/3 = 4 4/3 or 5 1/3

multiply 5 1/3 by 1/2

5 1/3 * 1/3 = 16/9 or 1 7/9

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3 years ago

Use the table below to answer this question:

tekilochka [14]

Using it's concept, it is found that the average rate of change of the function from x = -1 to x = 5 is of -1.

<h3>What is the average rate of change of a function?</h3>

It is given by the <u>change in the output divided by the change in the input</u>.

In this problem, the output changes by -6(from 7 to 1) when the input changes by 6(from -1 to 5), hence the average rate is given by:

r = -6/6 = -1.

More can be learned about the average rate of change at brainly.com/question/24313700

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2 years ago