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:
the answer for this sub-question is 43/90. This is assuming your teacher wants you to write it in fraction form. If she or he wants you to write it in decimal form, then 43/90 = 0.4778 approximately which converts to 47.78%
Answer in fraction form: 43/90
Answer in decimal form: 0.4778 (round this however you are instructed to)
Answer in percent form: 47.78% (round this however you are instructed to)
Step-by-step explanation:
Write and solve an equation of ratios:
x 9
---- = ----
16 x
Cross mult., we get x^2 = (16)(9)
Taking the sqrt of both sides, we get x = plus or minus (4)(3), or
x= plus or minus 12
Since x is measure of distance here, omit the -12 result. x = +12 units
Answer:
Well it would be 1 if 4b3c6 is what is actually given, but if it was (4b^3)(c^6) it would be 6 or if it was (4b)(3c^6), it'd still be 6
Answer:
8
Step-by-step explanation:
4x ÷ y
x = 1/2
y = 1/4
4(1/2) ÷ 1/4
4 × 1/2 = 2
2 ÷ 1/4
2 × 4 = 8
