Valeria is playing with her accordion. The length of the accordion A(t)A(t)A, left parenthesis, t, right parenthesis (in \text{c

To work with the repeating decimals, note that since there are two digits repeating, you will be using a 1 followed by two zeros, which is 100. This factor will be important for subsequent calculations.

Let’s denote the repeating decimal as x.

Thus, you can write

x = 0.212121...

Now, if you multiply this equation by 100, you can write it on top of the previous equation.
This results in:

100x = 21.212121...
x = 0.212121...

Next, set up a subtraction by taking the second equation from the first:

100x = 21.212121...
x = 0.212121...
- ----------------------------
99x = 21

Solving for x involves dividing both sides by 3:

33x = 7

Then, divide both sides by 33:

x = 7/33

Thus, we conclude that the repeating decimal 0.212121... equates to the fraction 7/33.

Answer: the fraction is 7/33

Answer:

Kindly present the graph.

Step-by-step explanation:

Response:

la respuesta está abajo

Explicación paso a paso:

Debemos encontrar la ecuación para poder graficar.

De acuerdo a la afirmación, la ecuación sería:

E = v * t - Ei

Siendo Ei (20) la elevación inicial, t el tiempo transcurrido y la velocidad de 4, realizamos la sustitución y obtenemos:

 E = 4 * t - 20

A continuación, debemos calcular los valores correspondientes:

E (0) = 4 * 0 - 20 = -20

E (1) = 4 * 1 - 20 = -16

E (2) = 4 * 2 - 20 = -12

E (3) = 4 * 3 - 20 = -8

E (4) = 4 * 4 - 20 = -4

E (5) = 4 * 5 - 20 = 0

Si graficamos, tendríamos la imagen anexa:

Response:

Part A

The best choice is;

b. y = 128(0.989)x + 72

Part B

Ella can consume the tea post 7:22

Detailed clarification:

Here, we observe the temperature variation with time represented in an exponential equation as follows;

Let the temperature at time x (measured in minutes) be y

Thus, y = a × mˣ + b

Where:

b = Curve shift or the limiting value of the decreasing exponential function as x → ∞

When y = 200, x = 0

This leads to 200 = a × m⁰ + c = a + c

Here, c represents the graph's shift, which is the temperature increase = final temperature = 72°F

Thus, a = 200 - 72 = 128°F

When y = 197, at x = 2 minutes

Thus, 197 = 128·m² + 72 =

m² = (197 - 72)/128 = 125/128

m = √(125/128) = 0.98821

Therefore, the exponential cooling equation is given by;

y = 128 × (0.98821)ˣ + 72

Hence the best choice is b. y = 128(0.989)x + 72

Part B

When the tea's temperature reaches 172°F, we have;

172 = 128 × (0.989)ˣ + 72

Thus, (0.989)ˣ = (172 - 72)/128 = 100/128 = 25/32

log(0.989)ˣ = log(25/32)

x·log(0.989) = log(25/32)

x = log(25/32)/log(0.989) = 22.32 minutes

Thus, Ella can consume the tea post 7:22.