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2 years ago

Someone please help me this is due in a few mintues ;-;

Mathematics

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postnew [5]2 years ago

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Answer:

4 2 and 3 are the exterior angles

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Solve the Anti derivative.

Alex Ar [27]

Answer:

$\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C$

General Formulas and Concepts:

Algebra I

Factoring

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Factor fraction denominator: $\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx$
[Integral] Integration Property - Multiplied Constant: $\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx$

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

$\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx$

Step 4: Integrate Pt. 2

[Integral] Substitute u-du: $\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C$
[Integral] Simplify: $\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C$
[integral] Multiply: $\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C$
[Integral] Back-Substitute: $\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C$

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

7 0

2 years ago

Lucinda leaves money in her savings account for 8 years. She started with $800 and earned 3.5% interest compound annually. How m

wariber [46]

I think she would have $1,058.07

8 0

2 years ago

Given that there are 28.3495 grams in an ounce, find the number of ounces in the heaviest item listed above.

weeeeeb [17]

The answer is actually C. 87.79 oz

3 0

3 years ago

Plz help will mark brainliest for the correct answer

Harlamova29_29 [7]

Ethans is the correct one

4 0

3 years ago

sofie and josh made 17 ounces of dough. they used 5/8 of the dough to make a pizza and used the rest to make calzones. what is t

fenix001 [56]

Answer=4.25 ounces or 4 1/4 ounces

17 ounces of dough

Amount used for pizza=17*5/8=10.625ounces

Amount used for calzones=17*3/8=6.375 ounces

amount used for pizza- amount used for calzones=
10.625-6.375=4.25ounces

4 0

3 years ago

Read 2 more answers