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3 years ago

What is the distance between the two numbers on a number line −7,−3 2/3

Mathematics

1 answer:

Nezavi [6.7K]3 years ago

7 0

Answer:

5/21

Step-by-step explanation:

Take -3/7 and -2/3 subtract them. (-3/7) - (-2/3) find a common denominator and alter fractions based on it. -9/21 + (14/21)

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I need help quick please

jok3333 [9.3K]

i’ll tell you on discord, add me there my user is ri#0511

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3 years ago

Read 2 more answers

What is the solution to the inequality below? <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%7D%20%20%5Cleqslant%205" id="T

ohaa [14]

Answer:

$x \leqslant \sqrt{5}$

Step-by-step explanation:

Hope this helped!

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20%5C%200%7D%20%5Cfrac%7B%5Csqrt%7Bcos2x%7D-%5Csqrt%5B3%5D%7Bcos3x%7D%20%7D%7

salantis [7]

Answer:

$\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}$

General Formulas and Concepts:

Calculus

Limits

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

L'Hopital's Rule

Differentiation

Derivatives
Derivative Notation

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:

We are given the limit:

$\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}$

When we directly plug in x = 0, we see that we would have an indeterminate form:

$\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}$

This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:

$\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}$

Plugging in x = 0 again, we would get:

$\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}$

Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:

$\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}$

Substitute in x = 0 once more:

$\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}$

And we have our final answer.

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

Unit: Limits

6 0

3 years ago

Which is a feature of a traditional IRA? There is no age limit for contributions. You can contribute until you're 70.5 years old

Crank

Hey there!

For a traditional IRA, you can only contribute until you're 70 and a 1/2 years old. There's no minimum age requirement to make any IRA contributions, but you must have a regular income that equals or exceeds your contribution.

Hope this helped you out! :-)

6 0

4 years ago

Read 2 more answers

Mrs. Kidd is five feet 3 inches tall. If one inch is approximately 2.5 centimeters, how many centimeters tall is Mrs. Kidd? Do N

Arturiano [62]

Answer:

Mrs.kidd is 162.5 centimeters tall

Step-by-step explanation:

5 foot 3 inches is 63 inches

63 times 2.5 = 162.5

Mrs.kidd is 162.5 centimeters tall

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3 years ago