To determine the rates at which the inlet and outlet pipes fill and empty the reservoir, we remember that work done equals rate multiplied by time. Let’s denote the inlet rate as i and for the outlet pipe as 0. Therefore,
i(24) = 1
o(28) = 1
In this context, the '1' represents the total number of reservoirs, since the problem states the time needed for each pipe to either fill or empty a singular reservoir. Solving for rates yields:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour
Over the first six hours, the inlet pipe fills (1/24)(6) = 1/4 reservoirs and during the same period, the outlet pipe empties (1/28)(6) = 3/14 reservoirs. To calculate the net volume of the reservoir filled, we subtract the emptying total from the filling total:
1/4 - 3/14 = 1/28 reservoirs (note that if emptying exceeds filling, a negative value results. In such cases, treat that negative value as zero, indicating that the outlet rate surpasses the inlet rate, leading to an empty reservoir).
Now we need to find out how long it will take to fill up one reservoir since we’ve already partially filled 1/28 of it, after closing the outlet pipe. In simpler terms, we need to determine the time required for the inlet pipe to finish filling the remaining 27/28 of the reservoir. Fortunately, we have already established the filling rate for the inlet pipe, leading to the equation:
(1/24)t = 27/28
Solving for t gives us 23.14 hours. Remember to add the initial 6 hours to this result since the question seeks the total time. Thus, the final total is 29.14 hours.
Please ask me any questions you may have!
Let h units denote the hypotenuse of the smaller triangle. From the Pythagorean Theorem, we derive specific relationships involving the smaller triangle with dimensions
along with the shorter leg of the second triangle denoted as s units. Furthermore, we apply the double angle property and substitute values to arrive at the final calculation.
18*2.50=45
50-45=5
Highlighters are priced at $3, which means she bought only one highlighter.
5-3=2
45+3=48
(The last 2 dollars likely account for tax)
Respuesta: Los contratos de opciones pueden ser valuados empleando modelos matemáticos tales como el modelo de precios Black-Scholes o el modelo Binomial. El costo de una opción se divide principalmente en dos componentes: su valor intrínseco y su valor temporal.... El valor temporal depende de la volatilidad anticipada del activo subyacente y del tiempo restante hasta que la opción expire.
Explicación paso a paso: ¡espero que esto ayude!
Por cierto, ¡también hablo inglés!
