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Ludmilka [50]
2 years ago
8

Cot 2 2x – 4cot2x + 3 = 0

Mathematics
1 answer:
jeyben [28]2 years ago
4 0

x = 9.21° or x = 22.5°

cot²2x – 4cot2x + 3 = 0

Let cot2x = y

y² - 4y + 3 = 0

Factorizing, we have

y² - y - 3y + 3 = 0

y(y - 1) -3(y - 1) = 0

(y - 1)(y - 3) = 0

y - 1 = 0 or y - 3 = 0

y = 1 or y = 3

Since cot2x = y

cot2x = 1 or cot2x = 3

1/tan2x = 1 or 1/tan2x = 3

tan2x = 1 or tan2x = 1/3

2x = tan⁻¹(1) or 2x = tan⁻¹(1/3)

2x = 45° or 2x = 18.43°

x = 45°/2 or x = 18.43°/2

x = 22.5° or x = 9.21°

So, x = 9.21° or x = 22.5°

Learn more about cotx here:

brainly.com/question/15546709

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Select the angle that correctly completes the law of cosines for this triangle. 72 + 252 – 2(7)(25)cos ___ = 242 A. 180° B. 90°
meriva

Answer:

x =76.45 degrees

Step-by-step explanation:

72 + 252 – 2(7)(25)cos _x__=242

combine like terms

324-350cosx = 242

subtract 324 from each side

-350x = -82

divide by -350

cos x = -82/-350

cos x = 82/350

take the arccos of each side

arccos (cos x) = arccos (82/350)

x =76.45 degrees


7 0
3 years ago
The annual rainfall (in inches) in a certain region is normally distributed with = 40 and = 4. What is the probability that star
sdas [7]

Answer:

0.93970

Step-by-step explanation:

Solution:-

- Denote a random variable "X" The annual rainfall (in inches) in a certain region . The random variable follows a normal distribution with parameters mean ( μ ) and standard deviation ( σ ) as follows:

                          X ~ Norm ( μ , σ^2 )

                          X ~ Norm ( 40 , 4^2 ).

- The probability that it rains more than 50 inches in that certain region is defined by:

                          P ( X > 50 )

- We will standardize our test value and compute the Z-score:

                          P ( Z > ( x - μ )  / σ )

Where, x : The test value

                          P (  Z > ( 50 - 40 )  / 4 )

                          P (  Z > 2.5 )

- Then use the Z-standardize tables for the following probability:

                          P ( Z < 2.5 ) = 0.0062

Therefore,          P ( X > 50 ) = 0.0062

- The probability that it rains in a certain region above 50 inches annually. is defined by:

                           q = 0.0062 ,

- The probability that it rains in a certain region rains below 50 inches annually. is defined by:

                           1 - q = 0.9938

                           n = 10 years   ..... Sample of n years taken

- The random variable "Y" follows binomial distribution for the number of years t it takes to rain over 50 inches.

                          Y ~ Bin ( 0.9938 , 0.0062 )

- The probability that it takes t = 10 years for it to rain:

                         =  10C10* ( 0.9938 )^10 * ( 0.0062 )^0

                         = ( 0.9938 )^10

                         = 0.93970

3 0
3 years ago
The number of students at maritas school decreased to 98 percent of last years number. Currently, there are 1,170 students. How
Salsk061 [2.6K]
1055 students were in the school last year
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Joe's employer will reimburse him $0.07 per mile driven. If Joe drives 179.53 miles on a business trip, what is his mileage reim
Reika [66]

Answer:

$12.27

Step-by-step explanation:

.07 times 179.53 is 12.5671 so rounded to 12.27

3 0
3 years ago
What is 1 2/3 times 4/5 in simplest form
Leviafan [203]

Answer:

Step-by-step explanation:

numerator x numerator

denominator x denominator

2 x 4=8

3 x 5=15

1 8/15

3 0
3 years ago
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