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3 years ago

Which decimal is larger. 1.3, 1.303, 1.33, 1.333

Mathematics

1 answer:

Nataly_w [17]3 years ago

4 0

Answer:

1.3

Step-by-step explanation:

1.33, 1.303, 1.333, 1.3

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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:

$v_1 = (x_1,y_1)$
$v_2 = (x_2,y_2)$

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

Does anyone know this?

rosijanka [135]

Answer:

-6

Step-by-step explanation:

Hello!

Since we are finding f(-1) we put -1 in for x

2(-1)^2 + 8(-1)

Follow PEMDAS

2 * 1 + 8(-1)

2 * 1 + -8

2 + -8 = -6

The answer is -6

Hope this helps!

7 0

4 years ago

1. Which of the following is most similar to a

Likurg_2 [28]

Answer:

D. An outline for a paper

Step-by-step explanation:

Think of a function like a template for numbers. You plug in numbers you know and you get a formula that is structured correctly. An outline is just like this because it is a structure for words.

8 0

3 years ago

2x2 + 12x – 3 = 0 <br> I don't know the steps and was wondering if I could get help.

Serhud [2]

2×2 then -3

I hope this can help

4 0

3 years ago

Read 2 more answers

identify the image of xyz for a composition of a 90 degree rotation and a 180 degree rotation, both about point x.

mariarad [96]

Answer: