Answer:
Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if 
. Recall that given two vectors a,b a⊥ b if and only if 
where 
is the dot product defined in 
. Suposse that 
. We want to find γ such that 
. Given that the dot product can be distributed and that it is linear, the following equation is obtained
Recall that 
are both real numbers, so by solving the value of γ, we get that
By construction, this γ is unique if 
, since if there was a 
such that 
, then
Answer:
x² - 16xy + 64y²
Step-by-step explanation:
The difference of x and 8y is x - 8y
The square of the difference is (x - 8y)² = (x - 8y)(x - 8y)
Expand by multiplying each term in the second factor by each term in the first factor, that is
x(x - 8y) - 8y(x - 8y) ← distribute both parenthesis
= x² - 8xy - 8xy + 64y² ← collect like terms
= x² - 16xy + 64y²
Answer:
A
Step-by-step explanation:
Answer:
76
Step-by-step explanation:
4^2 x 5^2 - 18^2
PEMDAS is our acronym for order of operations: Parentheses, exponents, multiplication, division, addition, subtraction.
Since we have no parentheses, we'll calculate the numbers and exponents (PEMDAS) first. "to the power of 2" is also called "squared" and means multiplying that number by itself.
(4x4) x (5x5) - (18x 18)
=16 x 25 - 324
Now we multiply: (PEMDAS)
= 400 - 324
then subtract: (PEMDAS)
=76
Answer:
C. The function is increasing when x > 0.
Step-by-step explanation:
