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Nimfa-mama [501]
3 years ago
13

Simplify: −4(b+6)−2b(1−4b

Mathematics
1 answer:
densk [106]3 years ago
3 0

Step-by-step explanation:

-4b-24-2b+8b2

8b2-6b-24=0

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Help evaluating the indefinite integral
Dafna11 [192]

Answer:

\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle (cu)' = cu'

Derivative Property [Addition/Subtraction]:
\displaystyle (u + v)' = u' + v'
Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:
\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

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

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx

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

<em>Identify variables for u-substitution/u-solve</em>.

  1. Set <em>u</em>:
    \displaystyle u = 4 - x^2
  2. [<em>u</em>] Differentiate [Derivative Rules and Properties]:
    \displaystyle du = -2x \ dx
  3. [<em>du</em>] Rewrite [U-Solve]:
    \displaystyle dx = \frac{-1}{2x} \ du

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Apply U-Solve:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du
  2. [Integrand] Simplify:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du
  3. [Integral] Rewrite [Integration Property - Multiplied Constant]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du
  4. [Integral] Apply Integration Rule [Reverse Power Rule]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C
  5. [<em>u</em>] Back-substitute:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

∴ we have used u-solve (u-substitution) to <em>find</em> the indefinite integral.

---

Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

---

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

Unit: Integration

5 0
2 years ago
A quality control inspector examined 200 light bulbs and found 16 defective . At this rate how many decfective bulbs would there
blondinia [14]
Ur answer is 1650 bulbs hope it helped
7 0
2 years ago
If 3 cups of rice serves 5 people, how many cups do you need to serve 13 people
elena-14-01-66 [18.8K]
First let's find out how many cups serve one person.

3 ÷ 5 = 1.6

1.6 of a cup serves one person.

1.6 × 13 = 20.8

It takes 20.8 (21 rounded) to serve 13 people.
3 0
3 years ago
Solve for x.
Oksanka [162]

Answer:

x = -4037/127

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

14x + 18 + x = -112(x + 36) + 13

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute -112:                         14x + 18 + x = -112x - 4032 + 13
  2. Combine like terms:                15x + 18 = -112x - 4019
  3. Add 112x on both sides;          127x + 18 = -4019
  4. Isolate <em>x</em> term:                          127x = -4037
  5. Isolate <em>x</em>:                                   x = -4037/127
3 0
3 years ago
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Gauge ran 12 miles in 20 minutes. What is Gaugue's hourly rate?
nikitadnepr [17]
36 miles per hour if he ran 12 miles in 20 minuets and there are 60 minuets in an hour, then multiply the # by 3
6 0
3 years ago
Read 2 more answers
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