Answer:
cos 2Ф = - 161/289 , tan 2Ф = - 240/161
Step-by-step explanation:
* Lets explain how to solve the problem
∵ cos Ф = - 8/17
∵ Ф lies in the 3rd quadrant
- In the 3rd quadrant sin and cos are negative values, but tan is
a positive value
∵ sin²Ф + cos²Ф = 1
∴ sin²Ф + (-8/17)² = 1
∴ sin²Ф + 64/289 = 1
- Subtract 64/289 from both sides
∴ sin²Ф = 225/289 ⇒ take √ for both sides
∴ sin Ф = ± 15/17
∵ Ф lies in the 3rd quadrant
∴ sin Ф = -15/17
∵ cos 2Ф = 2cos²Ф - 1 ⇒ the rule of the double angle
∵ cos Ф = - 8/17
∴ cos 2Ф = 2(-8/17)² - 1 = (128/289) - 1 = - 161/289
* cos 2Ф = - 161/289
∵ tan 2Ф = sin 2Ф/cos 2Ф
∵ sin 2Ф = 2 sin Ф × cos Ф
∵ sin Ф = - 15/17 and cos Ф = - 8/17
∴ sin 2Ф = 2 × (-15/17) × (-8/17) = 240/289
∵ cos 2Ф = - 161/289
∴ tan 2Ф = (240/289)/(-161/289) = - 240/161
* tan 2Ф = - 240/161
Answer:
He can make 11 bags.
Step-by-step explanation:
Every bag holds 1/2 pound.
He has 5 1/2.
He can make 11 bags for his chocolate.
hope this helps.
The sum of the distances of R to Q and P to Q is 9 units.
Solution:
Given points are P(–3, 6), Q(3, 6) and R(3, 3).
Distance between two points formula:

Distance from R to Q:
Here 
Substitute these in the given formula, we get
Distance =

= 3 units
Distance from R to Q is 3 units.
Distance from P to Q:
Here 
Substitute these in the given formula, we get
Distance =

= 6 units
Distance from P to Q is 6 units.
Sum of the distances = 3 + 6 = 9 units
Hence the sum of the distances of R to Q and P to Q is 9 units.