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
Given that the length of side of shaded area is 1 ft.
Making equal square of size of shaded area we have:
Horizontally number of shaded area are 12
Vertically number of shaded area are 11
So, the horizontal length of big rectangle is 12 ft.
The vertical length of big rectangle is 11 ft.
Area of big rectangle is 12*11
Area of given rectangle is 132 sq.ft.
Answer:
Step-by-step explanation:
We are asked the equation of the graph which passes through the points at (0,5) and (-3,-4).
Now, we know that the equation of a straight line passing through the points (
) and (
) is given by
.
So, in our case () ≡ (0,5) and () ≡ (-3,-4)
Therefore, the equation of the straight line will be
⇒ 
⇒ (Answer)
x=2y is linear and can also be writtend as y=x/2
1/8 of a quart would equal 1/4 of a pound
Hope this helps :)
