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:
Full explanation of what?
9514 1404 393
Answer:
║w║ = 6
Step-by-step explanation:
(c) The magnitude of w is computed the same way the magnitudes of the other vectors are computed. It is the root of the sum of the squares of the components.
║w║= ║<-6, 0>║ = √((-6)² +0²) = √36
║w║= 6
Answer:
Maricopa's Success invests $25,000 in stocks, $40,000 in bonds, and $10,000 in CDs.
Step-by-step explanation:
a = Stocks
b = Bonds
c = CDs
a + b + c = 75000
b = 30000 + c
a = 75000 - c - 30000 - c = 45000 - 2c
0.065(45000 - 2c) + 0.044(30000 + c) + 0.0225c = 3610
2925 - 0.13c + 1320 + 0.044c + 0.0225c = 3610
0.0635c = 635
c = 10000
So b = 40000 and a = 25000
