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3 years ago

Find the sum of the geometric series. a b c d

Mathematics

1 answer:

Musya8 [376]3 years ago

8 0

Answer:

B. $4\sqrt{3}-6$

Step-by-step explanation:

We have,

The first term of the series, $a=\sqrt{3}$ .

The common difference is given by, $r=\frac{\frac{-3}{2}}{\sqrt{3}}$ i.e. $r=\frac{-\sqrt{3}}{2}$ .

Since, the given series is an infinite series, then,

Sum of an infinite series = $\frac{a}{1-r}$

i.e. Sum the series = $\frac{\sqrt{3}}{1+\frac{\sqrt{3}}{2}}$

i.e. Sum the series = $\frac{2\sqrt{3}}{2+\sqrt{3}}$

i.e. Sum the series = $\frac{2\sqrt{3}}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}$

i.e. Sum the series = $\frac{2\sqrt{3}\times (2-\sqrt{3})}{4-3}$

i.e. Sum the series = $4\sqrt{3}-6$

Thus, the sum of the series is $4\sqrt{3}-6$ .

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Triangle ABC has coordinates A(-2, -3), B(1, 1), and C(2, -1). If the triangle is translated 4 units up, what are the coordinate

DochEvi [55]

Answer:

The coordinates of point A' will be: A'(-2, 0)

Step-by-step explanation:

We know that a translation is basically a transformation that occurs when an object is moved from one place to another place.

Translation does not change the size, orientation, or shape of the original object.

Translating a point P(x, y) 4 units up means we need to add to use P'(x, y+4), that is adding 4 units to the y-coordinate of the point P'(x, y).

Now we have to translate the triangle 4 units up. So, use the formula

P(x, y) → P'(x, y + 3)

Thus, the coordinates of point A' will be:

A(-2, -3) → A'(-2, -3+3) → A'(-2, 0)

Therefore, the coordinates of point A' will be: A'(-2, 0)

8 0

3 years ago

30 POINTS WILL GIVE BRAINLIEST

bonufazy [111]

12—— IT IS C ———————— thank me…!!!! Laterrrr!!!!

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3 years ago

1. A hotel manager buys 30 pillow cases and 25 shower curtains for $375. The manager then buys another 28 pillow cases and 35 sh

skad [1K]

Answer:

For #2: It's C. 17 nickels and 15 quarters.

Step-by-step explanation:

17*5= 85

15*25= 375

375+85= 460

add in the decimal:

17* 5 cents= $.85

15* 25 cents= $3.75

$3.75+ $.85= $4.60

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3 years ago

Write an equation for the graph. *slope intercept form*

Dennis_Churaev [7]

Answer:

y = 3x - 4

Step-by-step explanation:

The line crosses the y-axis at -4. The line goes 3 down and 1 left.

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3 years ago

Which equation has the solutions x = -3 ± √3i/2 ?

Maurinko [17]

Answer:Answer is option C : [ $x^{2}$ + 3x + 3 ] =0

Note: None of options matches with given question.

instead of "-3" , there should be "- $\frac{3}{2}$ ".

Step-by-step explanation:

Note: None of options matches with given question.

instead of "-3" , there should be " $\frac{3}{2}$ ".

Here, First thing you have to observe the nature of roots.

∴ x = - $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i and x = - $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$

∴ [ x+( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) ][ x+( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + x( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i)+ x( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i) + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ]=0

∴ [ $x^{2}$ + $\frac{3}{2}$ x + $\frac{\sqrt{3}}{2}$ ix + $\frac{3}{2}$ x - $\frac{\sqrt{3}}{2}$ ix + (3- $\frac{\sqrt{3}}{2}$ i)(3+ $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + ( $\frac{3}{2}$ - $\frac{\sqrt{3}}{2}$ i)( $\frac{3}{2}$ + $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ - ( $\frac{\sqrt{3}}{2}$ i)( $\frac{\sqrt{3}}{2}$ i) ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ - ( $\frac{3}{4}$ ) $i^{2}$ ] =0

∴ [ $x^{2}$ + 3x + $\frac{9}{4}$ + ( $\frac{3}{4}$ ) ] =0

∴ [ $x^{2}$ + 3x + $\frac{12}{4}$ ] =0

∴ [ $x^{2}$ + 3x + 3 ] =0

Thus, Answer is option C : <em>[ $x^{2}$ + 3x + 3 ] =0 </em>

6 0

4 years ago