Answer:
FIRST EXPRESSION:
- If 
, the value of 
is 
- If 
, the value of is 
- If 
, the value of is 
SECOND EXPRESSION:
- If , the value of 
is 
- If , the value of is 
- If , the value of is 
Yes, for any value of "b" the value of the first expression is greater than the value of the second expression.
Step-by-step explanation:
Substitute the given values of "b" into each expression and evaluate.
- For the first expression , you get:
If → 
If → 
If → 
- For the second expression , you get:
If → 
If → 
If → 
You can observe that for any value of "b" the value of the first expression is greater than the value of the second expression.
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:
n = -6
Step-by-step explanation:
2 ( n + 5 ) = -2
First, solve the brackets.
2n + 10 = -2
Now take 10 to the right side.
2n + 10 -10 = -2 - 10
2n = -12
Then divide both sides by 2.
And now you'll the value of n.
n = ( -6 )
n, n + 2, n + 4 - three consecutive even integers
3n = 2(n + 4) + 4 |use distributive property
3n = (2)(n) + (2)(4) + 4
3n = 2n + 8 + 4
3n = 2n + 12 |subtract 2n from both sides
n = 12
n + 2 = 12 + 2 = 14
n + 4 = 12 + 4 = 16
Answer: 12, 14, 16.
