FIND THE RATIONALIZING FACTOR OF THE FOLLOWING:<br><br><br>1)√ 2-√ 3 <br><br> 2)√ 12

Regular hexagon ABCDEF has vertices at A(4, 4!3), B(8, 4!3), C(10, 2!3), D(8, 0), E(4, 0) and F(2, 2!3).

marissa [1.9K]

Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:

$A=\frac{3\sqrt{3}}{2} a^2$

Where $A$ is the area of the regular hexagon

$a$ is the side length of the regular hexagon

Also, it's Perimeter is given by:

$P=6a$

Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.

A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.

Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.

Let us now find the distance between the points D and E using the distance formula which is as:

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Where $d$ is the distance.

$(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance $d$ )

Applying the above formula we get:

$d=\sqrt{(8-4)^2+(0-0)^2} =\sqrt{4^2}=4$

$\therefore d=4$

We know that this distance is the side length of the given regular hexagon.

$\therefore d=a=4$

Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:

$a_{small}=4-\frac{40}{100}\times 4=2.4$

Thus, the area of the smaller hexagon will be:

$A_{small}=\frac{3\sqrt{3}}{2} a_{small}^2=\frac{3\sqrt{3}}{2} (2.4)^2\approx14.96$ unit squared

and the new smaller perimeter will be:

$P_{small}=6a_{small}=6\times 2.4=14.4$ unit

Which are the required answers.

5 0

3 years ago

The velocity v and maximum height h of the water being pumped into the air are related by the equation v=\sqrt(2gh) where g is t

Whitepunk [10]

The velocity v and maximum height h of the water being pumped into the air are related by the equation

v= $\sqrt{2gh}$

where g = 32

(a) To find the equation that will give the maximum height of the water , solve the equation for h

v= $\sqrt{2gh}$

Take square root on both sides

$v^2$ = 2gh

Divide by 2g on both sides

$\frac{v^2}{2g}$ = h

So maximum height of the water h = $\frac{v^2}{2g}$

(b) Maximum height h= 80

velocity v= 75 ft/sec

Given g = 32

h = $\frac{v^2}{2g}$

h = $\frac{75^2}{2*32}$

h= 87.89 ft

The pump withe the velocity of 75 ft/sec reaches the maximum height of 87.89 feet. 87.86 is greater than the maximum height 80 feet.

So the pump will meet the fire department needs.

8 0

3 years ago

Mia is "helping" her mom pick up 27 toys that are strewn on the floor. Mia's mom puts five toys into the toy box every 40 second

dedylja [7]

Answer:

8 min

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5 0

2 years ago

The Charleston family has less than 500 Dalmatians. There are six times as many Dalmatians with black spots on their right ears

ANEK [815]

Let x be the number of Dalmatians without black spots.
So, x+6x is close to 500, which means x=71.
71*7=497, which is the total number of Dalmatians.
Giving away 6% of this will give you around 467 Dalmatians left.

Answer:467 Dalmatians

7 0

3 years ago

Read 2 more answers

La familia Sánchez Olguín, quiere terminar de construir su casa y necesita S/.25000 para todos los gastos del acabado de la casa

erastova [34]

Extraemos los datos del problema:

Capital Inicial → C₀ = S/.25000
Interés bimestral → i = 8 % = 0.08
Periodos → n = 3

<h2 /><h2>Bimestre 1:</h2>

Capital Inicial Bimestre → C = S/.25000

Tasa de interés bimestral:

I = C×i

I = S/.25000 × 0.08

I = S/.2000

Monto final:

M = C + I

M = S/.25000 + S/.2000

M = S/.27000

Variación Porcentual:

% = (M - C₀) / C₀

% = ( 27000 - 25000) / 25000

% = 8

<h2>Bimestre 2:</h2>

Capital Inicial Bimestre → C = S/.27000

Tasa de interés bimestral:

I = C×i

I = S/.27000 × 0.08

I = S/.2160

Monto final:

M = C + I

M = S/.27000 + S/.2160

M = S/.29160

Variación Porcentual:

% = (M - C₀) / C₀

% = ( 29160 - 25000) / 25000

% = 16.64

<h2>Bimestre 3:</h2>

Capital Inicial Bimestre → C = S/.29160

Tasa de interés bimestral:

I = C×i

I = S/.29160 × 0.08

I = S/.2332.8

Monto final:

M = C + I

M = S/.29160 + S/.2332.8

M = S/ 31492.8

Variación Porcentual:

% = (M - C₀) / C₀

% = ( 31492.8 - 25000) / 25000

% = 25.97

7 0

3 years ago

FIND THE RATIONALIZING FACTOR OF THE FOLLOWING:1)√ 2-√ 3 2)√ 12