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
57.6² = 33.8² + QR²
QR² = 2.175,32
QR = 46.64
57.6/sen90º = 46.64/sen(P)
sen(P) = 46.64*sen90º/57.6
sen(P) = 0.809
angle P is sen^-1 = 54.06º ≈ 54.1º
Area of a triangle is calculated by using the formula A=1/2bh
A= 1/2 (8.2) (5)
A=1/2 (41)
A=20.5 or 20 1/2, whichever way you think your teacher wants it.
Answer:
Step-by-step explanation:
The total amount of shrimp that was eaten was 12 pieces of shrimp.
To make the fraction you will simply put the amount of shrimp Jeremy ate over the total number of shrimp eaten by the pair.
Therefore, the fraction would look like this:
The decimal form of this would be 0.4167. Which also means that Jeremy ate 41.67% of the total amount of shrimp eaten.
Hope this helps!!
Answer:4x+12
Step-by-step explanation:
4 times x is 4x and 4 times 3 is 12
