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Tju [1.3M]
3 years ago
15

Expressions equal to 10^5

Mathematics
1 answer:
Drupady [299]3 years ago
6 0

Answer:

10 x 10 x 10 x 10 x 10, 20 x 20 x 10, 30 x 20

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What is the sum of the first seven terms of the geometric series 2 - 10 +50 -...?
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Answer:

26042.

Step-by-step explanation:

What's the first term of this geometric series?

2.

What's the common ratio of this geometric series?

Divide one of the terms with the previous term. For example, divide the second term -10 with the first term 2.

\displaystyle r = \frac{-10}{2} = -5.

What's the sum of this series to the seventh term?

The sum of the first n terms of a geometric series is:

\displaystyle a_1 \cdot \frac{1-r^{n}}{1-r},

where

  • a_1 is the first term of the series,
  • r is the common ratio of the series, and
  • n is the number of terms in this series.

\displaystyle 2 \times\frac{1- (-5)^{7}}{1- (-5)}=26,042.

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Step-by-step explanation:

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Provided<br> What is the value of 2 in the equation 60x = 360x
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A mouse climbs up a well of 86 meters. It advances 14 meters during the night, but during the day it retreats 2. The mouse will
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Step-by-step explanation:

we assume day and night are equally long.

and the mouse will start at night of day 1.

then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).

so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).

with a starting value of 14 (the first night).

so, we are getting an arithmetic sequence

an = an-1 + c

c = 12 in our case.

a1 = 14

a2 = a1 + 12 = 14+12 = 26

a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38

an = a1 + (n-1)×12 = 14 + 12(n-1)

at what n will it reach 86 ?

86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n

84 = 12n

n = 7

so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).

7 0
2 years ago
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