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2 years ago

11

Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary. log(x+9)-log x=3

1 answer:

zheka24 [161]2 years ago

4 0

(√6,0) (√5,-1) (-√6,0) (-√5,-1)

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According to Home Water Works, the average American shower uses 17.2 gallons and lasts about 8.2 minutes. To the nearest tenth o

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Home Water Works says that in most homes, showers are the third-largest user of water after toilets and clothes washers. The average American shower water usage is 17.2 gallons with the average shower length being 8.2 minutes. The average flow rate is 2.1 gallons per minute.

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What is the formula for the nth term of the given sequence 100, 20, 4, …

Naily [24]

Answer:

$a_n=100 \left(\dfrac15\right)^{n-1}$

Step-by-step explanation:

General equation of geometric sequence: $a_n=ar^{n-1}$

Given:

a₁ = 100
a₂ = 20
a₃ = 4

$\implies a_1=a=100$

$\implies a_2=100 \cdot r=20$

$\implies a_3=100 \cdot r^2=4$

Common ratio:

$r=\dfrac{a_3}{a_2}=\dfrac{4}{20}=\dfrac15$

Therefore:

$a_n=100 \left(\dfrac15\right)^{n-1}$

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