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3 years ago

My bathtub holds 21 gallons of water. How many pints of tomato juice do i need to fill my tub?

Mathematics

1 answer:

Alchen [17]3 years ago

7 0

Answer:

168

Step-by-step explanation:

21 x 8 pints in a gallon is 168

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Whats 2.638 rounded to the nearest hundredth?

OverLord2011 [107]

Answer:

2.64

Step-by-step explanation:

The 8 in the thousandths place can round up to .64

3 0

3 years ago

Damm [24]

Answer:

5x+10

Step-by-step explanation:

Hope this helps!!! :))

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3 years ago

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What is Limit of StartFraction StartRoot x + 1 EndRoot minus 2 Over x minus 3 EndFraction as x approaches 3?

scoray [572]

Answer:

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to c} x = c$

Special Limit Rule [L’Hopital’s Rule]:
$\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}$

Differentiation

Derivatives
Derivative Notation

Derivative Property [Addition/Subtraction]:
$\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:
$\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify given limit.

$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}$

Step 2: Find Limit

Let's start out by directly evaluating the limit:

[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \frac{\sqrt{3 + 1} - 2}{3 - 3}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \frac{\sqrt{3 + 1} - 2}{3 - 3} \\& = \frac{0}{0} \leftarrow \\\end{aligned}$

When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:

[Limit] Apply Limit Rule [L' Hopital's Rule]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\\end{aligned}$
[Limit] Differentiate [Derivative Rules and Properties]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \leftarrow \\\end{aligned}$
[Limit] Apply Limit Rule [Variable Direct Substitution]:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \leftarrow \\\end{aligned}$
Evaluate:
$\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \\& = \boxed{ \frac{1}{4} } \\\end{aligned}$

∴ we have evaluated the given limit.

___

Learn more about limits: brainly.com/question/27807253

Learn more about Calculus: brainly.com/question/27805589

___

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

3 0

2 years ago

Please take a look at the imageeeeeeeeeeeee

kramer

Answer:

I'm not alone

It's just me and your ghost

And this cripplin' depression

I thought I learned my lesson

But I threw out my phone

And I burned all your clothes

And now I'm not alone

It's just me and your ghost

[Verse 1]

I got four red bottoms up in flames at my place now (Place now)

I burned three Chanel dresses, three words we don't say now (Say now)

And it's hard not to drink when it's the one thing I think about

It's a lot of spiders in the attic, I don't mean to be dramatic

But I think it's kinda tragic who we magically became now

[Chorus]

I'm not alone

It's just me and your ghost

And this cripplin' depression

I thought I learned my lesson

But I threw out my phone

And I burned all your clothes

And now I'm not alone

It's just me and your ghost

[Post-Chorus]

Me and your ghost

Me and your ghost (Yeah)

[Verse 2]

Tell me what I'm s'posed to do with all these pictures on my iPhone

Even all them videos only you and I know

You never cared about me, you just care about the likes though

Every time you pop up, you should see my stupid eye roll

I can't even kick it with the homies that we both know

I can't even vist with any places that we used to go

Now all I got is just the memories of us though

Burn it all down to the ground with your ghost

[Chorus]

I'm not alone

It's just me and your ghost

And this cripplin' depression

I thought I learned my lesson

But I threw out my phone

And I burned all your clothes

And now I'm not alone

It's just me and your ghost

[Post-Chorus]

Me and your ghost

[Bridge]

I wish I could take back summer nights

Erase all the vibes

Leave the memories out to dry

Delete forever, no archive

Take the words you said to me

Hold on to them intentionally

I know that eventually

I'ma set fire to the one thing I love the most

Burn it all to the ground with your ghost

[Chorus]

I'm not alone

It's just me and your ghost

And this cripplin' depression

I thought I learned my lesson

But I threw out my phone

And I burned all your clothes

And now I'm not alone

It's just me and your ghost

[Post-Chorus]

Me and your ghost

Step-by-step explanation:

3 0

3 years ago

It takes a guinea pig about 68 days to develop comepletely before it is born. Which of these is less than 68 days

irakobra [83]

67 add the anwers though just so i can make sure

7 0

3 years ago

Read 2 more answers