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Mariulka [41]
3 years ago
10

What is the equation of the line that best fits the given data?

Mathematics
2 answers:
skad [1K]3 years ago
8 0
Your answer is A.) for ur problem
kupik [55]3 years ago
5 0
The correct answer would be option A
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Find two vectors in R2 with Euclidian Norm 1<br> whoseEuclidian inner product with (3,1) is zero.
alina1380 [7]

Answer:

v_1=(\frac{1}{10},-\frac{3}{10})

v_2=(-\frac{1}{10},\frac{3}{10})

Step-by-step explanation:

First we define two generic vectors in our \mathbb{R}^2 space:

  1. v_1 = (x_1,y_1)
  2. v_2 = (x_2,y_2)

By definition we know that Euclidean norm on an 2-dimensional Euclidean space \mathbb{R}^2 is:

\left \| v \right \|= \sqrt{x^2+y^2}

Also we know that the inner product in \mathbb{R}^2 space is defined as:

v_1 \bullet v_2 = (x_1,y_1) \bullet(x_2,y_2)= x_1x_2+y_1y_2

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

\left \| v_1 \right \|= \sqrt{x^2+y^2}=1

and

\left \| v_2 \right \|= \sqrt{x^2+y^2}=1

As second condition we have that:

v_1 \bullet (3,1) = (x_1,y_1) \bullet(3,1)= 3x_1+y_1=0

v_2 \bullet (3,1) = (x_2,y_2) \bullet(3,1)= 3x_2+y_2=0

Which is the same:

y_1=-3x_1\\y_2=-3x_2

Replacing the second condition on the first condition we have:

\sqrt{x_1^2+y_1^2}=1 \\\left | x_1^2+y_1^2 \right |=1 \\\left | x_1^2+(-3x_1)^2 \right |=1 \\\left | x_1^2+9x_1^2 \right |=1 \\\left | 10x_1^2 \right |=1 \\x_1^2= \frac{1}{10}

Since x_1^2= \frac{1}{10} we have two posible solutions, x_1=\frac{1}{10} or x_1=-\frac{1}{10}. If we choose x_1=\frac{1}{10}, we can choose next the other solution for x_2.

Remembering,

y_1=-3x_1\\y_2=-3x_2

The two vectors we are looking for are:

v_1=(\frac{1}{10},-\frac{3}{10})\\v_2=(-\frac{1}{10},\frac{3}{10})

5 0
3 years ago
In a school with 700 students, a survey revealed that 80% of the students liked the new lunch menu. Based on this data, how many
choli [55]

Answer:

560 students

Step-by-step explanation:

700 x 0.8 = 560

6 0
3 years ago
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X is a number so when u plus a letter that's still a number
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Which of the following points are on the line given by the equation y=1/2x
OLEGan [10]

Answer:

B, C, and F

Step-by-step explanation:

y = 1/2x

y = 1/2(4)

y = 2

y = 1/2x

y = 1/2(-2)

y = -1

y = 1/2x

y = 1/2(2)

y = 1

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Find Perimeter: SQUARE with sides that are each 5 inches in length
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If we’re talking 2d it would be 20inches, 3D it would be 120inches
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