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Sedaia [141]
3 years ago
6

When StartFraction 2 x squared Over y EndFraction = StartFraction w + 2 Over 4 EndFraction is solved for w, one equation is w =

StartFraction 8 x squared Over y EndFraction minus 2 Which of the following is an equivalent equation to find w?
Mathematics
1 answer:
Stells [14]3 years ago
8 0

Answer:

a

Step-by-step explanation:

taking the unit test rn lol

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Given that u =< 2,12 >, and z =< -7,5 >
swat32

Using the dot product:

For any vector x, we have

||x|| = √(x • x)

This means that

||w|| = √(w • w)

… = √((u + z) • (u + z))

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… = √(||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

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