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Luba_88 [7]
2 years ago
14

The value (in degrees) of each of the interior angles of a regular n-gon is represented by x. Write an inequality that describes

the minimum value of x.
Mathematics
2 answers:
saw5 [17]2 years ago
5 0

Answer:

180

Step-by-step explanation:

Sauron [17]2 years ago
3 0

Answer:

(n - 2)180 = x

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Which linear equation could David use to determine y, the total distance he could swim without stopping to rest?
Gala2k [10]

Answer:

I would say C

Step-by-step explanation:

because I think that 15 is the slope and the 35 is the y intercept. I could be wrong but that would be my guess

8 0
3 years ago
A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While
Murljashka [212]

Answer:

The expected number of appearance defects in a new car  = 0.64

standard deviation = 0.93(approximately)

Step-by-step explanation:

Given -

7% had exactly three, 11% exactly two, and 21% only one defect in cars.

Let X be no of defects in a car

P(X=3) = .07 , P(X=2) = .11 , P(X=3) = .21

P(X=0 ) = 1 - .07 - .11 - .21 = 0.61

The expected number of appearance defects in a new car =

E(X) = \nu = = \sum X P(X) =3\times 0.07 + 2\times0.11 + 3\times0.21 + 0\times0.61 = 0.64

\sigma^{2}  = variation of E(X) = \sum (X - \nu) ^{2}P(X) = (3 - 0.64) ^{2}\times0.07 + (2 - 0.64) ^{2}\times0.11 + (1 - 0.64) ^{2}\times0.21 + (0 - 0.64) ^{2}\times0.61

 = (2.36) ^{2}\times0.07 + (1.36) ^{2}\times0.11 + (.36) ^{2}\times0.21 + ( 0.64) ^{2}\times0.61 = 0.8704

standard deviation  =  \sqrt{\sigma^{2}} = \sqrt{0.8704^{2}} = 0.93(approximately)

4 0
3 years ago
12. When 64 is divided by x, the quotient is a negative
sergey [27]
J. -8 is the correct answer
8 0
2 years ago
Show me how much to shade
Gnoma [55]
If you're talking about inequality graphs, you shade the area where any point in the shaded area can solve the inequality, if I remember correctly. I can't exactly show you how much to shade.
3 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Cint%5Climits%5Ea_b%20%7B%281-x%5E%7B2%7D%20%29%5E%7B3%2F2%7D%20%7D%20%5C%2C%20dx" id="TexFo
Ludmilka [50]

Answer:\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(a) + 2a(1 - a^2)^\Big{\frac{3}{2}} + 3a\sqrt{1 - a^2}}{8} - \frac{3arcsin(b) + 2b(1 - b^2)^\Big{\frac{3}{2}} + 3b\sqrt{1 - b^2}}{8}General Formulas and Concepts:

<u>Pre-Calculus</u>

  • Trigonometric Identities

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Integration

  • Integrals
  • Definite/Indefinite Integrals
  • Integration Constant C

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

Integration Rule [Fundamental Theorem of Calculus 1]:                                    \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

U-Substitution

  • Trigonometric Substitution

Reduction Formula:                                                                                               \displaystyle \int {cos^n(x)} \, dx = \frac{n - 1}{n}\int {cos^{n - 2}(x)} \, dx + \frac{cos^{n - 1}(x)sin(x)}{n}

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx

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

<em>Identify variables for u-substitution (trigonometric substitution).</em>

  1. Set <em>u</em>:                                                                                                             \displaystyle x = sin(u)
  2. [<em>u</em>] Differentiate [Trigonometric Differentiation]:                                         \displaystyle dx = cos(u) \ du
  3. Rewrite <em>u</em>:                                                                                                       \displaystyle u = arcsin(x)

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

  1. [Integral] Trigonometric Substitution:                                                           \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[1 - sin^2(u)]^\Big{\frac{3}{2}} \, du
  2. [Integrand] Rewrite:                                                                                       \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos(u)[cos^2(u)]^\Big{\frac{3}{2}} \, du
  3. [Integrand] Simplify:                                                                                       \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \int\limits^a_b {cos^4(u)} \, du
  4. [Integral] Reduction Formula:                                                                       \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{4 - 1}{4}\int \limits^a_b {cos^{4 - 2}(x)} \, dx + \frac{cos^{4 - 1}(u)sin(u)}{4} \bigg| \limits^a_b
  5. [Integral] Simplify:                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4}\int\limits^a_b {cos^2(u)} \, du
  6. [Integral] Reduction Formula:                                                                          \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg|\limits^a_b + \frac{3}{4} \bigg[ \frac{2 - 1}{2}\int\limits^a_b {cos^{2 - 2}(u)} \, du + \frac{cos^{2 - 1}(u)sin(u)}{2} \bigg| \limits^a_b \bigg]
  7. [Integral] Simplify:                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}\int\limits^a_b {} \, du + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]
  8. [Integral] Reverse Power Rule:                                                                     \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3}{4} \bigg[ \frac{1}{2}(u) \bigg| \limits^a_b + \frac{cos(u)sin(u)}{2} \bigg| \limits^a_b \bigg]
  9. Simplify:                                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(u)sin(u)}{4} \bigg| \limits^a_b + \frac{3cos(u)sin(u)}{8} \bigg| \limits^a_b + \frac{3}{8}(u) \bigg| \limits^a_b
  10. Back-Substitute:                                                                                               \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{cos^3(arcsin(x))sin(arcsin(x))}{4} \bigg| \limits^a_b + \frac{3cos(arcsin(x))sin(arcsin(x))}{8} \bigg| \limits^a_b + \frac{3}{8}(arcsin(x)) \bigg| \limits^a_b
  11. Simplify:                                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(x)}{8} \bigg| \limits^a_b + \frac{x(1 - x^2)^\Big{\frac{3}{2}}}{4} \bigg| \limits^a_b + \frac{3x\sqrt{1 - x^2}}{8} \bigg| \limits^a_b
  12. Rewrite:                                                                                                         \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(x) + 2x(1 - x^2)^\Big{\frac{3}{2}} + 3x\sqrt{1 - x^2}}{8} \bigg| \limits^a_b
  13. Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:              \displaystyle \int\limits^a_b {(1 - x^2)^\Big{\frac{3}{2}}} \, dx = \frac{3arcsin(a) + 2a(1 - a^2)^\Big{\frac{3}{2}} + 3a\sqrt{1 - a^2}}{8} - \frac{3arcsin(b) + 2b(1 - b^2)^\Big{\frac{3}{2}} + 3b\sqrt{1 - b^2}}{8}

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

Unit: Integration

Book: College Calculus 10e

8 0
2 years ago
Read 2 more answers
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