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3 years ago

Question is in picture

Mathematics

1 answer:

yawa3891 [41]3 years ago

4 0

Answer:

Step-by-step explanation:

fairly simple x comes before y and in the top right its starts with (2,3) and you can clearly see close to the 0 (1,1)

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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

kims age is twice of her sister when you add to her sisters age you get 3 how old is each sister (a) write an equation that repr

Lina20 [59]

Kim is 2. Her sister is 1 years old. 2+1=3

6 0

3 years ago

Solve the following inequality: -20 < 4 - 2x A. 8 >x B. 8 C. 12 > x D. 12

Mama L [17]

Answer:

-20 < 4 - 2x (subtract 4 from both sides)

-24 < -2x (divide each side by -2)

12> x (when you divide by a negative number, the inequality flips)

x< 12 ( I always put it so x is first)

so the answer is C

6 0

2 years ago

Two Trains left a station at the same time. One traveled north at a certain speed and the other traveled south at twice that spe

sashaice [31]

Let s = northbound train
Then
2s = southbound train
:
Distance = time * speed
4s + 4(2s) = 600
:
4s + 8s = 600
:
12s = 600
:
s = 600/12
:
s = 50 mph is the northbound train
Then
2(50) = 100 mph is the southbound train
:
:
Check:
4(50) + 4(100) = 600

3 0

3 years ago

Read 2 more answers

Find the distance between the points ( - 10,12) and (15,12).

Nitella [24]

The distance formula is:

$d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

We are given two points in the form (x,y), so plug in the values to the distance formula:

$d= \sqrt{(-10-15)^2-(12-12)^2}$

Next we can simplify. We know that 12-12 is 0, so we can drop it from the equation, as it will not affect our answer. Also, we know that -10-15 is -25:

$d= \sqrt{(-25)^2}$

The square and square root cancel each other out leaving us with 25.

The answer is 25.

5 0

3 years ago