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andrew-mc [135]
3 years ago
13

Find the sum of the geometric series.

Mathematics
1 answer:
alexira [117]3 years ago
6 0

Answer:

Sum=\frac{32}{5}=6.4

Step-by-step explanation:

we are given geometric  series as

8-2+\frac{1}{2}-\frac{1}{8}+.......

we can use infinite sum formula

sum=\frac{a}{1-r}

where

a is first term

r is common ratio

so, we have

a=8

r=\frac{-2}{8}

r=-\frac{1}{4}

now, we can plug values

sum=\frac{8}{1-(-\frac{1}{4})}

Sum=\frac{32}{5}=6.4

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Write the slope-intercept form of the equation that passes through the point (4,-6) and is parallel to the line y = -3/4x - 5
Karolina [17]

The equation that runs through the location (4,-6) has the slope-intercept form,  y=-\frac{3}{4}x-3 .

<h2>Formation of the equation</h2>

A line's equation written in the slope-intercept form:

y=mx+b

where m= slope & b= y-intercept

The slope of two parallel lines is equal.

Currently, we know the line's equation:

y=-\frac{3}{4} x-5

here, slope, m= -\frac{3}{4}

A line equation is created by adding the slope's value and the point's coordinates (4, -6):

-6=-\frac{3}{4}(4)+b

⇒ -6=-3 +b [adding 3 to both sides]

⇒-3=b

⇒b= -3

Hence the solution is  y=-\frac{3}{4}x-3 .

Learn more about slope-intercept form here:

brainly.com/question/9682526

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5 0
1 year ago
A bamboo plant grows about 1.26 feet each
JulsSmile [24]

Answer:

8.82 feet in one week hopes it's helps

5 0
2 years ago
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When a number x is multiplied by 6, the result is 38 .
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X = 19/3

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6 0
3 years ago
Amelia launched her science fair rocket, and then backed away. The path of the rocket is given by the equation below, where y is
Mamont248 [21]

Answer:

1)The rocket hit the ground at     x = \frac{5}{4}

2)The maximum height of the rocket = 12.468 feet

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equation  

                y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

             \frac{dy}{dx} = -2( 2x) +5(1) =  -4x +5

Equating zero

            \frac{dy}{dx} = 0

⇒      -4 x +5 =0

⇒      -4 x = -5

⇒          x = \frac{5}{4}

<em> The rocket hit the ground at     </em>x = \frac{5}{4}<em></em>

<u><em>Step(ii):</em></u>-

    \frac{dy}{dx}  =  -4x +5  ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

 \frac{d^{2} y}{dx^{2} }  = - 4(1)

The maximum height at x = \frac{-5}{4}

  y = -2 x² + 5 x + 7

 y = -2 (\frac{5}{4})^{2}  + 5 (\frac{5}{4} )  + 7

y = \frac{-2(25)+ 25 (16)+7(64)}{64}

y = \frac{798}{64} = 12.468 feet

<em>The maximum height of the rocket = 12.468 feet</em>

       

4 0
2 years ago
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