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:
573.33
Step-by-step explanation:
599+14.33
= 573.33
(if rounding then its 600+14.33) = 614.33
Answer: 5.5 quarts = 22 cups
Step-by-step explanation:
1 cup = 4 cups
to convert cups to quart, just multiply by 4
5.5 x 4 = 22
3x + 2y=-10 equation 1
y=-x -4 equation 2
use the substitution method of elimination to get the answer to the question.
*using substitution
substitute equation 2 in one and we get
3x +2(-x-4)=-10
3x- 2x-8=-10
x=-2 and y=-2
Answer:
B
Answer:
d =2
Step-by-step explanation:
6d+8=14+3d
Subtract 3d from each side
6d-3d+8=14+3d-3d
3d +8 = 14
Subtract 8 from each side
3d +8-8 = 14-8
3d =6
Divide by 3
3d/3 = 6/3
d =2
