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PSYCHO15rus [73]
3 years ago
10

A charter airline finds that on its Saturday flights from Philadelphia to London all 160 seats will be sold if the ticket price

is $200. However, for each $3 increase in ticket price, the number of seats sold decreases by one.
Mathematics
1 answer:
Bas_tet [7]3 years ago
7 0

Missing part of the question is;

Find a formula for the number of seats sold if the ticket price is P dollars.

Answer:

(680 - P)/3

Step-by-step explanation:

A) Let x be equal to the number of seats and hence we can conclude that (160 - x) is equal to the number of seats after the increase in price.

Similarly, the increase in ticket price would be equal to (P - 200)

Due to the fact that for every $3 increase, the number of seats decrease by 1, the equation that links the change in the number of seats to the change in ticket price is;

P - 200 = 3(160 - x)

P = 3(160 - x) + 200

Making x the subject;

P = 480 - 3x + 200

P = 680 - 3x

3x = 680 - P

x = (680 - P)/3

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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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Masja [62]
8 Tatami mats are needed to cover the floor.
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Daniel, Clarence, and Matthew split a $20.20 dinner bill so that Daniel pays half of what
Bingel [31]

Answer:

8.80$

Step-by-step explanation:

Total 20.20. 6.06 x 2=12.12. 20.20-12.12=8.80$

Mathew paid 8.80$

Clarence paid 12.12$

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7 0
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Which of the following statements has the same truth value as the statement "If it is Friday, then Bruce has beans for supper."?
Andrews [41]

The contrapositive of the statement p ⇒ q is not q ⇒ not p and both the statements are equivalent.

So, the contrapositive of the statement "If it is Friday, then Bruce has beans for supper" is "If Bruce does not have beans for supper, then, it is not Friday"

This is the last statement given and is the answer.

7 0
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The angle θ 1 is located in Quadrant IV, and cos ⁡ ( θ 1 ) = 9/ 19 , theta, start subscript, 1, end subscript, right parenthesis
Firdavs [7]

Answer:

sin\theta_1 =  - \frac{2\sqrt{70}}{19}

Step-by-step explanation:

We are given that \theta_1 is in <em>fourth</em> quadrant.

cos\theta_1 is always positive in 4th quadrant and  

sin\theta_1 is always negative in 4th quadrant.

Also, we know the following identity about sin\theta and cos\theta:

sin^2\theta + cos^2\theta = 1

Using \theta_1 in place of \theta:

sin^2\theta_1 + cos^2\theta_1 = 1

We are given that cos\theta_1 = \frac{9}{19}

\Rightarrow sin^2\theta_1 + \dfrac{9^2}{19^2} = 1\\\Rightarrow sin^2\theta_1 = 1 - \dfrac{81}{361}\\\Rightarrow sin^2\theta_1 =  \dfrac{361-81}{361}\\\Rightarrow sin^2\theta_1 =  \dfrac{280}{361}\\\Rightarrow sin\theta_1 =  \sqrt{\dfrac{280}{361}}\\\Rightarrow sin\theta_1 =  +\dfrac{2\sqrt{70}}{19}, -\dfrac{2\sqrt{70}}{19}

\theta_1 is in <em>4th quadrant </em>so sin\theta_1 is negative.

So, value of sin\theta_1 =  - \frac{2\sqrt{70}}{19}

6 0
3 years ago
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