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:
27
Step-by-step explanation:
57 - 3 = 54. 54/2 = 27.
So easyies way is find all multiplues of 6 that are less than 50
6
12
18
24
30
36
42
48
and not 42
6
12
18
24
30
36
48
more than 25
30
35
48
do not have a 3 in them
48
the answer is 48
Answer:45
Step-by-step explanation:
Answer:
1/4x - 3 = 12
Step-by-step explanation:
When it says "three fewer," it means subtract three from one fourth of x. "Is" always means the equal sign. Knowing this, we get the equation:
1/4x - 3 = 12
