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Lemur [1.5K]
3 years ago
15

Find all solutions in the interval [0, 2π). 7 tan^3x - 21 tan x = 0

Mathematics
1 answer:
qwelly [4]3 years ago
4 0

To solve this problem, the first thing we can do is to take out 7 tan (x) from the whole equation, this results in simplification:

7 * tan (x) * (tan (x)^2 - 3) = 0 

Therefore the initial roots are taken from:

tan (x) = 0

Calculating for x:

x = 0, pi

 

The other roots can be taken from:

(tan (x)^2 - 3) = 0 

Calculating for x:

tan (x)^2 = 3

tan (x) = ± sqrt (3)  

x = pi/3 , 2pi/3 , 4pi/3 , 5pi/3 

 

Therefore the solutions are:

<span>0 , pi, pi/3 , 2pi/3 , 4pi/3 , 5pi/3 </span>

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Answer:

10.6

Step-by-step explanation:

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7 0
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What is the volume of a cylinder? Give an informal argument for the formula.
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3 0
3 years ago
Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all
posledela

This question is Incomplete

Complete Question

Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all have the same body size in their adult phase, which made it easy to measure speeds in units of body lengths per second (bl/s). The researchers found that, when traffic is light and not congested, ant speeds vary roughly Normally, with mean 6.20 bl/s and standard deviation 1.58 bl/s. (a) What is the probability that an ant's speed in light traffic is faster than 5 bl/s? You may find Table B useful. (Enter your answer rounded to four decimal places.)

Answer:

0.7762

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

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x = 5 bl/s

z = 5 - 6.20/1.58

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The probability that an ant's speed in light traffic is faster than 5 bl/s is P( x > 5)

Probability value from Z-Table:

P(x<5) = 0.22378

P(x>5) = 1 - P(x<5)

= 1 - 22378

= 0.77622

Approximately to 4 decimal places = 0.7762

The probability that an ant's speed in light traffic is faster than 5 bl/s is 0.7762

5 0
3 years ago
Round to the nearest hundredth 5/8
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stealth61 [152]
X^2-5x+5x-25 (multiply (x-5) with (x+5))
X^2-25 ( -5x+5x =0)





5 0
3 years ago
Read 2 more answers
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