Usando la tasa conjunta, se encuentra que se tardaría 2.4 horas en llenarse la piscina con los dos grifos a la vez.
<h3>¿Cuál es la tasa conjunta?</h3>
La tasa conjunta es la suma de cada tasa por separado.
En este problemas, las tasas por separadas són dadas por 1/6 y 1/4. Por eso, la <em>tasa conjunta</em> es dada por:
![\frac{1}{x} = \frac{1}{6} + \frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%20%3D%20%5Cfrac%7B1%7D%7B6%7D%20%2B%20%5Cfrac%7B1%7D%7B4%7D)
![\frac{1}{x} = \frac{2 + 3}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%20%3D%20%5Cfrac%7B2%20%2B%203%7D%7B12%7D)
![\frac{1}{x} = \frac{5}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D%20%3D%20%5Cfrac%7B5%7D%7B12%7D)
![5x = 12](https://tex.z-dn.net/?f=5x%20%3D%2012)
![x = 2.4](https://tex.z-dn.net/?f=x%20%3D%202.4)
Se tardaría 2.4 horas en llenarse la piscina con los dos grifos a la vez.
Puede-se aprender más a cerca de la tasa conjunta en brainly.com/question/25159431
<span> graph of y = [x] for -2 ≤ x ≤ 2 </span>
Answer:
Center: (2,-1)
Radius: 4 units
Step-by-step explanation:
Equation of the circle in standard form is:
![x^{2}+y^{2}+2gx+2fy+c=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D%2B2gx%2B2fy%2Bc%3D0)
The radius of this circle is located at (-g, -f) and its radius is equal to:
![r=\sqrt{g^{2}+f^{2}-c}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bg%5E%7B2%7D%2Bf%5E%7B2%7D-c%7D)
The given equation of circle is:
![x^{2}+y^{2}-4x+2y-11=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D-4x%2B2y-11%3D0)
Re-writing this equation in a form similar to the standard equation:
![x^{2}+y^{2}+2(-2)x+2(1)y-11=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2By%5E%7B2%7D%2B2%28-2%29x%2B2%281%29y-11%3D0)
Comparing this equation with standard equation we can say:
g= -2
f = 1
c = -11
So, the center of the circle will be located at (-g, -f) = (2, -1)
And the radius will be = ![\sqrt{g^{2}+f^{2}-c} =\sqrt{(-2)^{2}+(1)^{2}-(-11)} =\sqrt{16} =4](https://tex.z-dn.net/?f=%5Csqrt%7Bg%5E%7B2%7D%2Bf%5E%7B2%7D-c%7D%20%3D%5Csqrt%7B%28-2%29%5E%7B2%7D%2B%281%29%5E%7B2%7D-%28-11%29%7D%20%3D%5Csqrt%7B16%7D%20%3D4)
Thus the radius of the given circle is 4 units.
The equation of the line in the form y = mx + b are as follows:
<h3>How to find the equation of a line?</h3>
The equation of a line can be found as follows:
Using the slope intercept form,
y = mx + b
where
Therefore, let's find the slope using the table.
(-4, 13)(-3, 11)
m = 11 - 13 / -3 + 4
m = - 2 / 1
m = -2
Let's find the y-intercept using (-4, 13)
13 = -2(-2) + b
13 - 4 = b
b = 9
Therefore, the equation of the line is y = -2x + 9
Using the second table,
(0, -3)(2, 1)
m = 1 + 3 / 2 - 0
m = 4 / 2
m = 2
y-intercept = b = -3
Therefore,
the equation of the line is y = 2x - 3
learn more on equation of a line here:brainly.com/question/27665802
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