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:
A. a quadratic function can only have one y-intercep
Answer:
14 gallons....$42
Step-by-step explanation:
The car requires one gallon every 32 miles...
The car requires c gallons for 448 miles
c = 448 × 1 / 32
= 14 gallons..
One gallon = $3
Fourteen gallons = ??
14 × 3 / 1 = $42
Answer:
40
Step-by-step explanation:
Let n represent the integer. Then the increase can be written as ...
n + (-12) = 28
We can add 12 to both sides of this equation:
n + (-12) + (+12) = 28 +12
n + 0 = 40 . . . . . . -12 and 12 total to zero; 28 and 12 total to 40.
n = 40
The integer is 40.