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vivado [14]
3 years ago
8

I need some help answering some fractions.

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
3 0
1. 2/8
2. 3/4
3. 1/3
4. 4/5
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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:

<u>Algebra I</u>

  • Factoring

<u>Calculus</u>

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:

<u>Step 1: Define</u>

<u />\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx<u />

<u />

<u>Step 2: Integrate Pt. 1</u>

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

<u>Step 3: Identify Variables</u>

<em>Set up u-substitution for the arctan trig integration.</em>

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

<u>Step 4: Integrate Pt. 2</u>

  1. [Integral] Substitute u-du:                                                                               \displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du
  2. [Integral] Trig Integration:                                                                               \displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C
  3. [Integral] Simplify:                                                                                           \displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C
  4. [integral] Multiply:                                                                                           \displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C
  5. [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
Which is the correct answer?
Montano1993 [528]

Answer:

I'm not sure but I think it is letter A

Step-by-step explanation:

Because first off 0 is divisible by any integer number meaning it has to be divide by a whole number not fraction. Also, 0 + 2 = 2 then you divide that by 4 is 0.5.

6 0
3 years ago
Which is a factor of 21?<br> 4<br> 3<br> 6<br> 5
arsen [322]

Answer:

3

Step-by-step explanation:

Using listing:

1 \times 21 = 21

3 \times 7 = 21

No other factors are possible.

Hence, 1, 3, 7 and 21 are factors of 21.

3 0
3 years ago
Read 2 more answers
HELP HELP PLEASE the height of the triangle is 16 cm, and fe=10 cm. What is the area of the triangle? A. 50 CM^2 B. 80 CM^2 C.16
enyata [817]

Answer:

B. 80 cm^2

Step-by-step explanation:

A = bh/2

A = (FE)(16 cm)/2

A = (10 cm)(16 cm)/2

A = 80 cm^2

4 0
2 years ago
8over 20= y over 60 what is y
Pachacha [2.7K]
The answer to the problem is 24
6 0
3 years ago
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