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4 years ago

Introduction to addition of fractions with different denominator 3/5+1/3

Mathematics

1 answer:

Anna35 [415]4 years ago

3 0

It would be 4/8 because if u add 3+1 its 4 and if u add 5+3 it equals 4/8

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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

liubo4ka [24]

Answer:

sad

Step-by-step explanation:

6 0

3 years ago

Suppose you have a triangle with only 1 median drawn. Without constructing its other 2 medians, explain how you can locate the c

djyliett [7]

9514 1404 393

Answer:

trisect the median. The centroid is 1/3 its length from the side.

Step-by-step explanation:

The centroid divides each median into parts with a ratio of 2:1. If you trisect the median, the centroid will be 1 unit from the side and 2 units from the vertex.

8 0

3 years ago

Suppose you are going to graph the data in the table:

beks73 [17]

Answer:

A: x‒axis: minutes in increments of 5; y-axis: temperature in increments of 1

Step-by-step explanation:

Let the x-axis represent the minutes

Let the y-axis represent the temperature

Now, from the values given us in minutes, we can see that the difference between the values are Increasing at constant rate of 5 minutes .

Thus, minutes increment on the x-axis is 5.

Now,for the y-axis, the increment is not constant as it fluctuates.

Thus, we cannot use 5 like we did for the x-axis. Rather, the most appropriate temperature increment to be used on this y-axis for ease of locating the points will be 1.

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3 years ago

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Is 3/2 greater than 1

Romashka-Z-Leto [24]

Yes. 3/2 is equivalent to 1.5

7 0

3 years ago

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