Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
Answer:
X=6
Y= - 1
Step-by-step explanation:
X-y =7
X+y =5 cross - y and y
_______
X+x =7 +5
2x= 12
X= 12/2
X= 6
Replace X in first equation:
X - y =7
6 - y =7
6 - 7 =y
y = - 1
Hope this helps you.. Good Luck!
Common Ratio<span>. For a </span>geometric sequence<span> or </span>geometric series<span>, the </span>common ratio<span> is the ratio of a term to the previous term. This ratio is usually indicated by the variable r.</span>
Answer:
fixed - monthly rent, car payment, savings for new guitar
variable - movies, video games, snacks
Step-by-step explanation:
Fixed costs are costs that do not vary with output.
the amount of rent paid is fixed.
Variable costs are costs that vary with production
the amount paid at the movies depend on the number of movies watched
