Answer:
The simplest form is tan(4x)
Step-by-step explanation:
* Lets revise the identity of the compound angles
- 
- 
* Lets solve the problem
- Let 9x = 5x + 4x
∴ tan(9x) = tan(5x + 4x)
- Use the rule of the compound angle
∵ 
⇒ (1)
∵ 
⇒ (2)
∵ tan(9x) = equation (2)
- Substitute (2) in (1)
∴ 
- Multiply up and down by (1 - tan(5x)tan(4x))
∴ ![\frac{tan(5x)+tan(4x)-tan(5x)[1-tan(5x)tan(4x)]}{1-tan(5x)tan(4x)+tan(5x)[tan(5x)+tan(4x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%285x%29%2Btan%284x%29-tan%285x%29%5B1-tan%285x%29tan%284x%29%5D%7D%7B1-tan%285x%29tan%284x%29%2Btan%285x%29%5Btan%285x%29%2Btan%284x%29%5D%7D)
- Simplify up and down
∴ 
∴ ![\frac{tan(4x)+tan^{2}(5x)tan(4x)}{[1+tan^{2}(5x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%284x%29%2Btan%5E%7B2%7D%285x%29tan%284x%29%7D%7B%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D)
- Take tan(4x) as a common factor up
∴ ![\frac{tan(4x)[1+tan^{2}(5x)]}{[1+tan^{2}(5x)]}](https://tex.z-dn.net/?f=%5Cfrac%7Btan%284x%29%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D%7B%5B1%2Btan%5E%7B2%7D%285x%29%5D%7D)
- Cancel [1 + tan²(5x)] up and down
∴ The answer is tan(4x)
Answer:
The answer is: y = 3x - 7
Step-by-step explanation:
Given point: (5, 8).
Slope m = 3
Use the point slope form and solve for y:
y - y1 = m(x - x1)
y - 8 = 3(x - 5)
y - 8 = 3x - 15
y = 3x - 15 + 8
y = 3x - 7
Proof:
f(x) = 3x - 7
f(5) = 3(5) - 7
= 15 - 7 = 8, giving (5, 8)
Considering the desired result of the hypothesis test, we the closest mean time to 1.5 hours, hence the correct option is:
C. 1.6 hrs
<h3>What should be the mean?</h3>
The closer the mean is to the sample mean, the less likely we are to reject the null hypothesis.
In this problem, the sample mean is of 1.5 hours, hence, the closest value, considering the absolute value of the difference, is of 1.6 hours, hence option C is correct.
More can be learned about the test of an hypothesis at brainly.com/question/16313918
A ) The rate at which rumor spreads speed up over time. If t increases, also N(t) increases, because 300 is divided by the smaller number.( Correct )B ) 1 = 300 / ( 1 + 299 · e^(-0.36 · 0 ) ) 1 = 300 / ( 1 + 299 · 1 ) 1 = 300 / 3001 = 1 ( Correct )C ) 100 = 300 / ( 1 + 299 · e^(-0.36 · 14 ) )100 = 300 / ( 1 + 299 · 1/154.47 )100 = 300 / 2.93565100 ≈ 102.192 ( Correct ) - approx. 14 minutes
D ) N = 300 / ( 1 + 299 · e^(-∞) )N = 300 / ( 1 + 299 · 0 ) N = 300 / 1 = 300299 people are enclosed space ( Not correct )Answer:True statements are: A ) , B ) and C ) .
