Length of outer boundary =30m
So area of outer boundary =30×30
= 900m²
Length of inner boundary of path=30-1= 29m
Inner area =29×29 =841m²
So area of path is= outer area - inner area
=900- 841
= 59m²
Answer:
7a+b-9c+17d
Step-by-step explanation:
-5 ( a-2b+3c -4d) - (-3) (4a -3b+2c-d)
Distribute
-5a+10b-15c+20d+12a-9b+6c-3d
Combine like terms
7a+b-9c+17d
2400miles/60hours
40miles/hour
Answer is D
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
