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nirvana33 [79]
3 years ago
11

Tanisha went to the store to buy some chicken. The price per pound of the chicken is $5.75 per pound and she has a coupon for $2

off the final amount. With the coupon, how much would Tanisha have to pay to buy 4 pounds of chicken? Also, write an expression for the cost to buy pp pounds of chicken, assuming at least one pound is purchased.
Mathematics
1 answer:
abruzzese [7]3 years ago
7 0

Answer:

$21

Step-by-step explanation:

Part 1

5.75 x 4 = 23

23 - 2 = 21

Part 2.

5.75x - 2

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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

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Step-by-step explanation:

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3 years ago
Pleaseeee answer quickly i need it
Nataly_w [17]
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