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:
2232 for 170 minutes
Step-by-step explanation:
To know the mass of the sphere given the density , we first define density as
D = Mass / volume
now we have a value of density but doesn't have volume so we compute for it using the given radius 5.5 cm
V = <span>(4/3)πr^3
so
mass = D (volume)
mass = 11.34 (</span>(4/3)π(5.5)^3 )
mass = 7902.96 g <span>Hope my answer would be a great help for you.
If </span>you have more questions feel free to ask here at Brainly.
<span> </span>
5/7. Use rise over run it helps
<u>Answers</u>
The function has a domain of all real numbers . True
<em>The cube root of real number is also real. The negative sign is outside he radical so it cannot result to an imaginary number.</em>
The function is a reflection of y =³√x . True
The function is always increasing. False
<em>When getting the cube root of a number the result is alway smaller. So the domain of the function should be decreasing not increasing.</em>
The function has a range of {y|– < y < } . False
The function passes through the point (3, –27) . False
<em>When this values are substituted it the function they don't satisfy it. </em>
