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
Since you have a angle number of 23 and you see the tiny square that means it’s equal to 90 up top and add 23 and 90 together and then subtract that by 180 to get all 3 angles in the triangle and then just use that to find the other line that’s 180.
Answer: see my work
Step-by-step explanation:
volume is lwh
volume is 3*3*10
volume is 9*10
volume is cubic cm
volume is 90
volume is 90 cubic cm
Tan(58)=10/x
x=10/tan(58)
x= 6.2
Answer:
c = 1.45
Step-by-step explanation:
Solving the equation for c, we find ...
p +e = nc
c = (p +e)/n
Filling in the values given, we have ...
c = (4050 +300)/3000 = 4350/3000 = 1.45
The value of c is 1.45.
