A simulation is a mathematical model used to represent a situation.
- A simulation can be a program or a physical test to "simulate" a situation to predict the outcomes.
When we combine two or more simple events we have a compound event
- "Compound" means to combine, like a compound word would be a combination of two words
A Tree Diagram is a diagram that shows all the possible outcomes of an event
- In a tree diagram, each possible outcome "branches" off the main stem, making the final diagram look like a tree with many separating branches.
All the possible outcomes or results is called the sample space
- The outcomes are each different samples, and a sample space is a space that collects each of these samples
When an event is not affected by a previous outcome we have an independent event
- This event is "independent", not affected by other factors, making it an independent event
Let me know if you need any clarifications, thanks!
~ Padoru
The banner would be 10feet 3inches
Between 1 and 2 would be decimals.
E.g: 1.1, 1.2,1.3 etc
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
