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3 years ago

A recursive rule for a geometric sequence is a1=3;an=12an−1 . What is the explicit rule for this sequence?

1 answer:

6 0

From the recursive rule, you can tell the initial value is 3 and the common ratio is 12. The explicit rule is always
.. (n-th term) = (initial value)*(common ratio)^(n -1)

Subsituting the values you know, you have
.. an = 3*12^(n-1)

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2 years ago

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3 years ago

If I can walk 9673.6 meters in 5 hours. How far can I walk in 70 minutes. ( I need the work)

den301095 [7]

First, convert 5 hours into minutes:

5 hours 60 min

------------ * --------------- = 300 min

1 1 hr

Next, find the unit rate in m/min:

9673.6 m

--------------- = 32.24 m/min

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Now find the distance you can walk in 70 minutes at this rate:

32.24 m

------------- * 70 min = 2247 meters (answer)

1 min

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3 years ago

1. What are foci? 2. What is the first step to take to write the equation of a hyperbola? 3. How do you represent parts of a hyp

Andrei [34K]

Answer: see below

<u>Step-by-step explanation:</u>

1) Foci is plural for Focus. Since a hyperbola has two focus points, they are referred to as foci. The foci is where the sum of the distances from any point on the curve to the foci is constant.

2) When determining the equation of a hyperbola you need the following:

a) does the hyperbola open up or to the right?

b) what is the center (h, k) of the hyperbola?

c) What is the slope of the asymptotes of the hyperbola?

3) The equation of a hyperbola is:

$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1$

(h, k) is the center of the hyperbola
± b/a is the slope of the line of the asymptotes
The equation starts with the "x" if it opens to the right and "y" if it opens up

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3 years ago

Jason is traveling by car from his home to his office. He has gone 3.5 miles so far. From this point on, he can cover 100 miles

Elden [556K]

First the equation needs to be set to "y" to find the total amount of miles traveled:
y=
Then you know he has already gone 3.5, this is a constant and can be added to the graph immediately
y=3.5
Then you know every two hours he can cover 100 miles, which means 50 miles per hour or 50 per x, so add 50x to 3.5 to show that he will go 3.5 miles plus 50 miles for every hour he is traveling.
y=3.5+50x

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3 years ago