Help meeeeeeeeeeeeee

The lenght of diving board is 378 cm what i the lenght in meters

Virty [35]

Answer: 37.8

Step-by-step explanation:

a meter is ten less so so u would divied

5 0

3 years ago

HELP!!!! Divide. Write your answer in lowest terms as a proper or improper fraction (not a mixed number). 11/21 divided by 22/7

vodomira [7]

My answer is 1/6. Here's How I worked it out:

11/21 / 22/7 is the same as or = to 11/21 * 7/22 which = 77/462 and then divide both the numerator and denominator by 77 and you get 1/6. (In other words simplify 77/462). Hope this helped :)

8 0

4 years ago

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

below is a diagram showing a regular hexagon and a regular Pentagon. Each shape has a lengths of two sides shown in the terms of

Strike441 [17]

To solve this, we work out the perimeter of the hexagon, by finding x, and we work out the perimeter of the pentagon by find y, and the compare them:

Perimeter of the Hexagon:
Since it is a regular hexagon, all the sides are the same: This means we can say that:

4x - 2 = x + 4 (Now lets solve this)
4x = x + 6 ( Add both sides by 2 to get 4x alone)
3x = 6 (Subtract both sides by x, to collect the x values)
x = 2     (Divide both sides by 3 to get what just x is)

Now we work out the length of one side by substituting the value for x in
x + 4 = 2 + 4
= 6

Now that we know the length of one side, we can multiply that by 6 to get the perimeter, because a hexagon has six sides.

6 * 6 = 36

Perimeter of the Pentagon
Since it is a regular Pentagon, all the sides are the same, just like the hexagon. This means we can say that:

5y - 8 = 2y + 1    (Now we solve this like we did before)
5y = 2y + 9 ( Add both sides by 8 to get 5y alone)
3y = 9    (Subtract both sides by 2y, to collect the y values)
y = 3 (Divide both sides by 3 to get what just y is)

Now we work out the length of one side by substituting the value for x in
2y + 1 = (2 * 3) + 1
= 7

Now that we know the length of one side, we can multiply that by 5 to get the perimeter, because a pentagon has 5 sides.

5 * 7 = 35

Since the perimeter of the hexagon is 36, and the perimeter of the pentagon is 35, we can see that:

The hexagon has the larger perimeter.

5 0

4 years ago

Chapter 5 • Measures of Central Tendency | 171

Black_prince [1.1K]

Answer: Rs. 5,033.30

Step-by-step explanation:

Total employees = 15 + 32 + 65 + 79 + 90 + 57 + 36 + 14 = 388

Median position = 388/2 = 194

Median therefore lies in range where cumulative employees is 194:

= 15 + 32 + 65 + 79 = 191

Median therefore lies in range after 4,000 - 4,999 which is 5,000 - 5,999.

Median = Lower limit of median range + range of median range * (median position - cumulative frequency up to median range) / frequency of median range

= 5,000 + 999 * (388/2 - 191)/90

= 5,000 + 33.3

= Rs. 5,033.30

8 0

3 years ago