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
For either one of the deals, just find what one card equals and times it by how many cards the other equation has.
e.g. 0.35 cents divide by 10 = 0.035. And now, you times it by 12 since the other deal is 12 cards for 40 cents.
0.035 x 12 = 0.48
So, 10 cards for 35 cents is not the better deal.
Answer:
growth
Step-by-step explanation:
This is of the form
y = ab^x where a is the initial value and b is either growth or decay
if b > 1 then it is growth
b <1 it is decay
a = .2
b = 4
Since b>1 it is growth
Answer:
Decimal - 0.19 Fraction - 19/100
Step-by-step explanation:
