There are 72 green pens.
There is 9 times as many white pens from 2 to 18, so there has to be 9 times as many green pens because of the ratio. 9 times 8 is 72.
Difference would be 1000x3.0 - 8.8x10000 = -85000
Scientific notation would be 8.5x10^-4
Answer:
Step-by-step explanation:
Givens
Let the width = x
Let the length = x + 5
Equation
2w + 2W = P
Solution
2x + 2(x + 5) = 192 Remove the brackets <=== Answer
2x + 2x + 10 = 192 Combine like terms
4x + 10 = 192 Subtract 10 from both sides
4x = 192 - 10
4x = 182 Divide by 4
4x/4 = 182/4
x = 45.5
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
