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HACTEHA [7]
2 years ago
12

5p+2= -10 Show your work

Mathematics
1 answer:
Monica [59]2 years ago
5 0

Answer:

p= -12/5

Step-by-step explanation:

you have to subtract 2 from both sides

5p+2(-2)=-10 (-2)

5p= -12

5p/5= -12/5

p= -12/5

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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 cyclist travels 7.7 km in 30 minutes. <br> What is his average speed in km/h?
NARA [144]
60 min = 1 hr
30 times 2 = 60 minutes
7.7 times 2 = 15.4 km
15.4 km per hr is the answer

PLEASE MARK BRAINLIEST
4 0
3 years ago
If y varies directly as x and y=3 when x=2 find y when x=8​
satela [25.4K]

Answer:

12

Step-by-step explanation:

x=2 was multiplied by 4 to get to x=8 so you multiply y=3 by 4 to make it y=12

6 0
3 years ago
Read 2 more answers
How to figure it out
ElenaW [278]
Im not 100% sure but 
A: 10
B: 5     
C: 15
D: 30 
for:
A: 30 x 1/3 
B: 15 x 1/3
C: 5/ 1/3
D: 10/ 1/3 
5 0
3 years ago
Read 2 more answers
How do you Round 96,286 to the nearest thousand.
Varvara68 [4.7K]

Answer:

The correct answer is 96,000

Step-by-step explanation:

To round you look at the thousands place and there is a 9 then you look at the number to the right of it which is 2 and it is lower than 5 since it is lower than five it rounds down so the correct answer is 96,000.

HAVE A GOOD DAY!

8 0
3 years ago
Read 2 more answers
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