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2 years ago

15

Hii. if Lisa was going 9.2 miles from the store to her friends house then 7.9 to her grandmas house before going 5 miles to her

house how far did she travel?

1 answer:

STALIN [3.7K]2 years ago

4 0

Answer:

¹9.2

<u> +7.9 </u>

¹ 17.1

<u> +5.0</u>

22.1

21.1 miles

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Which of the sums below can be expressed as 6(3 + 9)?<br> 18 + 54<br> 18 +9<br> 09 + 15<br> 6 + 54

Zinaida [17]

Answer: 18+54

Step-by-step explanation:

6*3=18 and 6*9=54

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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?

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Answer:

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

General Formulas and Concepts:

<u>Calculus</u>

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:

<u>Step 1: Define</u>

<em>Identify given limit</em>.

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

<u>Step 2: Find Limit</u>

Let's start out by <em>directly</em> 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 <em>evaluated</em> the given limit.

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

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

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

Unit: Limits

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1 year ago

The function y=−0.25x+0.55 represents the percent y (in decimal form) of battery power remaining x hours after you turn on a lap

AURORKA [14]

Answer: a is 2.2, b is 0.55
Explanation:
To find the x intercept, put 0 instead of y,
hence,
0=-0.25x+0.55
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To find y intercept put 0 instead of x,
so,
y=-0.25*0+0.55
y=0+0.55
y=0.55

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3 years ago

A company makes wax candles in the shape of a solid sphere. Suppose each candle has a diameter of 15 cm. If

jekas [21]

We have been given that a company makes wax candles in the shape of a solid sphere. Each candle has a diameter of 15 cm. We are asked to find the number of candles that company can make from 70,650 cubic cm of wax.

To solve our given problem, we will divide total volume of wax by volume of one candle.

Volume of each candle will be equal to volume of sphere.

$V=\frac{4}{3}\pi r^3$ , where r represents radius of sphere.

We know that radius is half the diameter, so radius of each candle will be $\frac{15}{2}=7.5$ cm.

$\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot (7.5\text{ cm})^3$

$\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot 421.875\text{ cm}^3$

$\text{Volume of one candle}=1766.25\text{ cm}^3$

Now we will divide 70,650 cubic cm of wax by volume of one candle.

$\text{Number of candles}=\frac{70,650\text{ cm}^3}{1766.25\text{ cm}^3}$

$\text{Number of candles}=\frac{70,650}{1766.25}$

$\text{Number of candles}=40$

Therefore, 40 candles can be made from 70,650 cubic cm of wax.

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3 years ago

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