Answer:
Step-by-step explanation:
First, simplify each term:
Then given expression is equivalent to
![\cos ^3\alpha+(-\sin \alpha)^3-(-\sin \alpha)+(-\cos \alpha)\\ \\=\cos ^3\alpha-\sin^3 \alpha+\sin \alpha-\cos \alpha\\ \\=(\cos\alpha-\sin\alpha)(\cos^2\alpha+\cos\alpha\sin\alpha+\sin^2\alpha)-(\cos\alpha-\sin\alpha)\\ \\=(\cos\alpha-\sin\alpha)(1+\cos\alpha\sin\alpha-1)\ \ [\cos^2\alpha+\sin^2\alpha=1]\\ \\=\cos\alpha\sin\alpha(\cos\alpha-\sin\alpha)](https://tex.z-dn.net/?f=%5Ccos%20%5E3%5Calpha%2B%28-%5Csin%20%5Calpha%29%5E3-%28-%5Csin%20%5Calpha%29%2B%28-%5Ccos%20%5Calpha%29%5C%5C%20%5C%5C%3D%5Ccos%20%5E3%5Calpha-%5Csin%5E3%20%5Calpha%2B%5Csin%20%5Calpha-%5Ccos%20%5Calpha%5C%5C%20%5C%5C%3D%28%5Ccos%5Calpha-%5Csin%5Calpha%29%28%5Ccos%5E2%5Calpha%2B%5Ccos%5Calpha%5Csin%5Calpha%2B%5Csin%5E2%5Calpha%29-%28%5Ccos%5Calpha-%5Csin%5Calpha%29%5C%5C%20%5C%5C%3D%28%5Ccos%5Calpha-%5Csin%5Calpha%29%281%2B%5Ccos%5Calpha%5Csin%5Calpha-1%29%5C%20%5C%20%5B%5Ccos%5E2%5Calpha%2B%5Csin%5E2%5Calpha%3D1%5D%5C%5C%20%5C%5C%3D%5Ccos%5Calpha%5Csin%5Calpha%28%5Ccos%5Calpha-%5Csin%5Calpha%29)
Answer:
The number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E is 10,080 ways
Step-by-step explanation:
We need to find the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E.
There are 9 letters in the word WONDERFUL
There is a condition that letter R is always next to E.
So, We have two letters fixed WONDFUL (ER)
We will apply Permutations to find ways of arrangements.
The 7 letters (WONDFUL) can be arranged in ways : ⁷P₇ = 7! = 5040 ways
The 2 letters (ER) can be arranged in ways: ²P₂ =2! = 2 ways
The number of ways 'WONDERFUL' can be arranged is: (5040*2) = 10,080 ways
So, the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E is 10,080 ways
I honestly have no clue i just need to answer a question do i can ask my question that i needed help with,
Answer:
748.23 in^2.
Step-by-step explanation:
Area = 1/2 * apothem * perimeter
= 1/2 * 14.7 * 101.8
= 748.23 in^2.
Answer:
Left angle = 60°
Top angle = 120°
Right angle = 60°
Step-by-step explanation:
Use what you know about angle relationships to set up equations you can solve for each variable.
The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.
You have two variables, so you need at least two equations (I made three but only used two).
The work is in my attachment, comment of you have questions.
