Answer:
The answer is 7.2368421053 .
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
10936.1 yards = 10 kilometers 1 kilometer = 1093.1 yards
6 x 9 = 54
He has a total of 54 pages to grade.
54 - 12 = 42 pages
He still has to grade 42 pages.
Hope I helped!!
Answer:
Did you copy this down correctly?
Step-by-step explanation:
b = .125 which is rational
a is irrational because the square root of a prime number is irrational.
If c = 225....
then adding 2 rational numbers = rational sum
But adding (or multiplying) an irrational number to a rational number = irrational number.
