Answer:
Step-by-step explanation:
Consider a quadratic equation given by
.... (1)
The quadratic formula then is
The quadratic equation provided is
This can be expressed as
.... (2)
By comparing (1) and (2), we derive:
Plug these values into the quadratic formula.
Factoring out common elements.
The two solutions are
and 
We recognize that
Thus,
Consequently, root is positive while is negative.
The provided equation is a differential equation that allows for variable separation. You should group similar terms, integrate, use the correct limits, and present V as a function of t. This is achieved in the following manner: dV/dt = -3(V)^1/2, which rearranges to dV/-3V^1/2 = dt. Initially, when V equals 225, after integration, we arrive at -2/3(√V - √225) = t, which can be further detailed as -2/3(√V - 15) = t. This represents the function for V at a specific time t. I trust this information is helpful, have a pleasant day.
Answer:
Aproximadamente 428 N
Step-by-step explanation:
Peso = 1,500 * 9.8 = 14,700 N
Densidad = Masa ÷ Volumen
1,030 = 1,500 ÷ V
V = 1,500 ÷ 1,030 = 1.46 m^3.
La fuerza de flotación = Densidad * g * V
La fuerza de flotación = 1,000 * 9.8 * (1,500 ÷ 1,030)
La fuerza de flotación = 9,800 * (1,500 ÷ 1,030) = 14,272 N.
La fuerza neta = 14,700 – [(9,800 * (1,500 ÷ 1,030)]
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!
1) Equilateral Triangles: Triangles of this type have uniformly equal side lengths and angles. Therefore, if the side measurements are identical, the triangle is categorized as equilateral.
2) Isosceles Triangles: Such triangles feature two sides of the same length, with the third side differing. Given this, if the provided side lengths include two equal sides, it is classified as an isosceles triangle.
3) Scalene Triangles: These triangles have all sides of differing lengths. When all side lengths are distinct, it indicates a scalene triangle.
I hope this explanation is helpful!:)
