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:
Step-by-step explanation:
Y= X - 4
Hope this helps!
Thanks for Brainliest!
Answer:
less likely
Step-by-step explanation:
Lower probability = lower chance to happen
0.3 is less than 0.4
Answer:
1875 arrangements
Step-by-step explanation:
Break-Even is the point when costs are equal to profit.
The cost is 15,000
We need to cover this up with the profit we get from sales.
Each arrangement is 17 (cost) and is sold for 25, so the profit from each arrangement is:
25 - 17 = 8
So, with each arrangement sale, we make profit of $8. How many of these we need to sell in order to break even (in order to make 15,000)??
We simply divide this amount (15,000) by the profit we make from each arrangement ($8), so that would be:
Number of Arrangements Needed to Break-Even = 15,000/8 = 1875
After 1875 arrangements, the boutique breaks even.
