$GEOMETRIC \: \: PROGRESSIONS \\ \\ \\\\Taking \: \: L.H.S. \: \\ \\ 0.999... \: = \: 0 \: + \: \frac{9}{10} \: + \: \frac{9}{100} \: + \: \frac{9}{1000} + \: ... \: \: \infty \\ \\ \\ 0.999... \: = \: \frac{9}{10} \: ( \: 1 \: + \frac{1}{10} \: + \: \frac{1}{100} \: + \: \frac{1}{1000} + \: ... \: \: \infty \: \: ) \\ \\ \\ 0.999... \: = \: \frac{9}{10} \: ( \: 1 + \: \: \frac{1}{ {10}^{1} } \: + \: \frac{1}{ {10}^{2} } \:+ \: \frac{1}{ {10}^{3} } \: + \: ... \: \: \infty \: ) \\ \\ \\ As \: we \: can \: see \: \: , \: \\ \\ Above \: expression \: in \: bracket \: forms \: a \: \\ Infinite \: Geometric \: Progression \\ \\ Where \: \: ,\: \: \: \: \\ a = 1 \: \: \: \: \: and \: \: \: \: \: r = \frac{1}{10} \\ \\ Sum \: of \: Infinite \: Geometric \: \\ Progression \: \: = \: \: \frac{a}{1 - r} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{1 - \frac{1}{10} } \: \: = \: \: \frac{1}{ \frac{9}{10} } \: \: = \: \: \frac{10}{9} \\ \\ \\ Putting \: in \: above \: , \: we \: get \: - \: \\ \\ 0.999... \: \: = \: \: \frac{9}{10} \times \frac{10}{9} \: \: \\ \\ \\ 0.999... \: \: = \: \: 1 \: \: = \: R.H.S. \\ \\ Hence , \: above \: expression \: is \: TRUE \: \: :)$

7 0

3 years ago

In order to determine the height of the flagpole in the school yard, Cindy is going to use similar triangles. The

kvv77 [185]

The height of the pole is 12.5 feet.

<h3>What is Unitary method?</h3>

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Cindy's shadow is 5 feet.

length of the shadow of the pole at the same time, she finds it to be 12.5 feet.

So,

12.5/5=x/5,

62.5=5x

x= 12.5 feet.

Hence, the height of the pole is 12.5 feet.

Learn more about this Unitary method here:

brainly.com/question/22056199

#SPJ1

4 0

2 years ago

1) -15 - 47 = 3(7-7)

lidiya [134]

What is the question?

5 0

3 years ago

Philip has $2,000 & spends $23.75 on supplies. He divides the remaining amout equally among his 8 employees. How much does e

Brut [27]

Answer:

247.03125

Step-by-step explanation:

Subtract: 2000 - 23.75 = 1976.25

Divide: 1976.25 / 8 = 247.03125

Hope this helps!

4 0

3 years ago