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vlada-n [284]
3 years ago
12

Determine whether the series -20 + 100 - 500 + ... is convergent or divergent.

Mathematics
2 answers:
irinina [24]3 years ago
7 0

Answer:

B

Step-by-step explanation:

practice on edg 2021

storchak [24]3 years ago
3 0

it's divergent, you can actually simplify this series by combining terms in pairs

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Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction p
kirza4 [7]

The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

<h3>How to convert sine of an angle to some angle of cosine?</h3>

We can use the fact that:

\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)

to convert the sine to cosine.

<h3>Which trigonometric functions are positive in which quadrant?</h3>
  • In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
  • In second quadrant(π/2 < θ < π), only sin and cosec are positive.
  • In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
  • In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

y= 3\cos(2(x + \pi/2)) - 2

The options are:

  1. y= 3\sin(2(x + \pi/4)) - 2
  2. y= -3\sin(2(x + \pi/4)) - 2
  3. y= 3\cos(2(x + \pi/4)) - 2
  4. y= -3\cos(2(x + \pi/2)) - 2

Checking all the options one by one:

  • Option 1: y= 3\sin(2(x + \pi/4)) - 2

y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

  • Option 2: y= -3\sin(2(x + \pi/4)) - 2

This option if would be true, then from option 1 and this option, we'd get:
-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0

which isn't true for all values of x.

Thus, this option is not same as the given function.

  • Option 3: y= 3\cos(2(x + \pi/4)) - 2

The given function is y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2

This option's function simplifies as:

y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2

Thus, this option isn't true since \sin(2x) \neq \cos(2x) always (they are equal for some values of x but not for all).

  • Option 4: y= -3\cos(2(x + \pi/2)) - 2

The given function simplifies to:y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2

The given option simplifies to:

y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2

Thus, this function is not same as the given function.

Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

Learn more about sine to cosine conversion here:

brainly.com/question/1421592

4 0
2 years ago
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1. Locate a menu for your favorite restaurant and pick three items for yourself and each friend.
ddd [48]

Answer:

Wat the heck?

Step-by-step explanation:

Is this hw cus I feel bad for ya!

6 0
3 years ago
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Is (4, 2) a solution to the equation y = x2 − 7x?
sergey [27]

Answer:

not rlly

Step-by-step explanation:

you need more information to solve that type of equation

8 0
2 years ago
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What expressions are equivalent to (a^2-16)(a+4)
Eddi Din [679]

Answer:

[(a)^2-(4^2)](a+4)

Step-by-step explanation:

7 0
2 years ago
PLEASE I AM BEGGING help me all I need to so is show work I have to turn this in tmrw pls​
GenaCL600 [577]

Hello and Good Morning/Afternoon:

<u>Let's take this problem step-by-step</u>:

<u>Let's consider all the information given</u>:

  1. Eddie's pension is based on the average of his last four year's salaries

           \hookrightarrow \text{average } = \text {sum of all salaries} / \text{ number of years}\\ \hookrightarrow \text{average}= 392000 / 4 = 98000

   

      2. The employer will pay 1.2% of that average for each year he worked

            \hookrightarrow \text{1.2 percent of average} = \frac{1.2}{100} *98000=1176

      3. The employer will therefore pay in total

             \hookrightarrow \text{Total pension} = 1176 * 20 \text{ years} = 23520

<u>Answer: $23520</u>

<u></u>

Hope that helps!

#LearnwithBrainly

6 0
1 year ago
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