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
X = y + 12. You then substitute or plug in that from the first equation into the second equation. You get (y+12)+y=18, then you simplify to get your y value. In this case y = 3. The you can plug your y value into either equation. (x+3=18) or (x-3=12) or (x=3+12) either way you get x=15 and y=3.
Answer:
the correct answer is D
Step-by-step explanation:
5 x 1,021 = 5,105
Answer:
(x-1)(x-1) and (x-3)(x+2)
Step-by-step explanation:
Answer:
okay
Step-by-step explanation:
