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Delvig [45]
3 years ago
10

Solve 2 cos theta + 2 = 3 in the interval from 0 to 2pi. Round to the nearest hundredth.

Mathematics
1 answer:
TiliK225 [7]3 years ago
4 0
2cos theta = 1 -> cos theta = 1/2

Then theta = pi/3 + 2npi or -pi/3 + 2npi, where n is random interger

And the domain is restricted in [0,2pi]

So answer will be pi/3 or 5pi/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

7 0
3 years ago
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luda_lava [24]
1.) (-3,-2)
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6 0
3 years ago
It take 10 road workers 5 days to complete a road repair when working 2 hours a day.Working at the same Pace, how many days will
ludmilkaskok [199]

Answer:

The workers will need 10 days to finish the job.

Step-by-step explanation:

To solve this question we can use a compound rule of three. We have:

10 road workers -> 5 days -> 2h/day

2 road workers ->  x days -> 5h/days

The first thing we should do is analyze how the proportions between the variables work, if they're inversely or directly proportional. If we raise the number of workers we expect that the amount of days needed to finish the job lowers and if we raise the number of hours worked in a day we expect that the workers would need less days to finish the job. So we need to invert the fractions that are inversely proportional to the amount of days worked, then we have:

2 -> 5 -> 5

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x = (5*2*10)/(2*5) = 100/10 = 10 days

8 0
3 years ago
Cherries cost 4 dollars per pound. Mother bought r lbs and father bought 2 lbs. How much more money did mother spend on cherries
vazorg [7]

T=  the total cost

T=4r+2

4 0
3 years ago
Read 2 more answers
If f(x) = 4x + k and f (2) = f (1), then calculate the value<br>of K.​
andrezito [222]

Answer:

-7

Step-by-step explanation:

given f(x)=4x+k

therfore, f(2)=4*2+k

we know that f(2) =1

so, 4*2+k=1

8+k=1

k=1-8

k=-7

8 0
3 years ago
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