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Nookie1986 [14]
4 years ago
15

Without using a calculator, order the following numbers from least to greatest. 5 39 6

Mathematics
1 answer:
mote1985 [20]4 years ago
8 0

Answer:

5, 6, 39

Step-by-step explanation:

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Orthogonalizing vectors. Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, a
jeka57 [31]

Answer:

\\ \gamma= \frac{a\cdot b}{b\cdot b}

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 b \neq 0. Recall that given two vectors a,b  a⊥ b if and only if a\cdot b =0 where \cdot is the dot product defined in \mathbb{R}^n. Suposse that b\neq 0. We want to find γ such that (a-\gamma b)\cdot b=0. Given that the dot product can be distributed and that it is linear, the following equation is obtained

(a-\gamma b)\cdot b = 0 = a\cdot b - (\gamma b)\cdot b= a\cdot b - \gamma b\cdot b

Recall that a\cdot b, b\cdot b are both real numbers, so by solving the value of γ, we get that

\gamma= \frac{a\cdot b}{b\cdot b}

By construction, this γ is unique if b\neq 0, since if there was a \gamma_2 such that (a-\gamma_2b)\cdot b = 0, then

\gamma_2 = \frac{a\cdot b}{b\cdot b}= \gamma

6 0
3 years ago
Brad wants to open a new savings account. He finds one that returns 3% on his investment each year.
Rufina [12.5K]

Answer:

  • final balance: A
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Step-by-step explanation:

The variable assigments can be anything you like. It is often helpful to use variables that will remind you what they stand for. Here, we have chosen A = amount (final balance); P = principal (initial investment); r = rate.

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