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3 years ago

Consider the arithmetic sequence:

Mathematics

2 answers:

tatyana61 [14]3 years ago

7 0

Answer:

d(n)=8+2n for n >1

Step-by-step explanation:

I check on khan

prisoha [69]3 years ago

4 0

Answer:

Answer: D

Step-by-step explanation:

Arithmetic Sequences

The arithmetic sequences are those where any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

$a_n=a_1+(n-1)r$

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

We are given the arithmetic sequence:

10, 12, 14, 16, ...

Where a1=10 and

r = 12 - 10 = 2

Thus the general term is:

$a_n=10+(n-1)2$

Operating:

$a_n=10+2n-2$

$a_n=8+2n$

Answer: D

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ivanzaharov [21]

Answer:

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Step-by-step explanation:

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 6800 cm³/min,

dV/dt = k - 6800

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

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dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

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k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

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Zanzabum

Answer:

$755.98 ft^2$

Step-by-step explanation:

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