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taurus [48]
3 years ago
14

Can someone help please show steps

Mathematics
1 answer:
NikAS [45]3 years ago
4 0

Hello!

\large\boxed{-16}

Use PEMDAS (order of operations) to solve:

-4 · [3 + (-5)²] ÷ 7

Square -5:

-4 · [3 + 25] ÷ 7

Add the numbers inside of the parenthesis:

-4 · [28] ÷ 7

Multiply -4 and 28:

-112 ÷ 7

Divide:

= -16.

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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
Who has insta gramm I really need help with my assignments I need good grades to graduate
galina1969 [7]

Answer:

just search on brainly thats what im doing are you onine schooling

Step-by-step explanation:

6 0
3 years ago
Write an equation in slop-intercept form the line with slope 1/4 and y-intercept -7
Licemer1 [7]

When you write an equation in the slope-intercept form

y=mx+b

the two coefficients m and b represent, respectively, the slope and the intercept.

So, in your case, m=1/4 and b= -7, which leads to the equation

y=\dfrac{1}{4}x-7

7 0
3 years ago
Can you help me please I’ll give brainliest
kolezko [41]
The answer is B I hope it’s right
5 0
2 years ago
Can someone help me please
Lisa [10]

Answer:

perimeter is 12x-6

Step-by-step explanation:

perimeter is the sum of all sides

3(x+2) + 2x+11 + 7x-23

distribute the 3 in the first term, then combine 'like terms'

3x+6 + 2x+11 + 7x-23

3x+2x+7x + 6+11+(-23)

12x-6

4 0
2 years ago
Read 2 more answers
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