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EleoNora [17]
3 years ago
8

Shiloh and her friends spent the day at an amusement park. In the first hour, they rode two rides. After 2 hours, they had ridde

n 4 rides. They had ridden 6 rides after 3 hours.
Write a function to represent the arithmetic sequence.
f(n)=
Mathematics
1 answer:
solmaris [256]3 years ago
4 0

Answer:

The function will be: f(n) = 2n

Step-by-step explanation:

An arithmetic sequence is a sequence where the common difference between consecutive terms is same

The sequence according to given information is:

2,4,6...

Here

a_1 = 2

a_2 = 4

a_3 = 6

the common difference will be:

d = a_2-a_1 = 4-2 = 2\\d = a_3-a_2 = 6-4 = 2

The arithmetic sequence is given by:

a_n = a_1+(n-1)d

Putting the values

a_n = 2+(n-1)(2)\\a_n = 2+2n-2\\a_n = 2n

Hence,

The function will be: f(n) = 2n

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21. Given the pattern below, which recursive formula represents the number of triangles in this sequence?
Tamiku [17]

Answer:

its 4

Step-by-step explanation:

a 1 = 3 , a n = a n - 1 + 2

because if you aply this to the shapes that you see at problem 21 you will see that it meaches them

6 0
2 years ago
A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and
goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}

Solve for S(t):

\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}

e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}

The left side is the derivative of a product:

\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}

Integrate both sides:

e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt

e^{t/800}S(t)=64e^{t/800}+C

S(t)=64+Ce^{-t/800}

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

0=64+C\impleis C=-64

and so (b) the amount of sugar in the tank at time t is

S(t)=64\left(1-e^{-t/800}\right)

As t\to\infty, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

7 0
3 years ago
100% =3200<br>70% = ????​
SVEN [57.7K]

Answer:

2240

Step-by-step explanation:

plz fo"ow ms

mark me as brainlist

4 0
2 years ago
Read 2 more answers
If y varies inversely as x and y = 27 when x = 12 , find x when y = - 9 .
Sergio039 [100]

Answer:

x = - 36

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = \frac{k}{x} ← k is the constant of variation

To find k use the condition y = 27 when x = 12, then

k = yx = 27 × 12 = 324, thus

y = \frac{324}{x} ← is the equation of variation

When y = - 9, then

- 9 = \frac{324}{x} ( multiply both sides by x )

- 9x = 324 ( divide both sides by - 9 )

x = - 36

3 0
3 years ago
Find a formula for a function f(x,y,z) whose level surface f=81 is a sphere of radius 9, centered at the origin.
Mrrafil [7]

81(9 \times 8 = 72 + 9) = 81
4 0
3 years ago
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