How to solve 2x-3x=6 5x+4y=12
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The equation of the hyperbola is :
The center of a hyperbola is located at the origin that means at (0, 0) and one of the focus is at (-50, 0)
As both center and the focus are lying on the x-axis, so the hyperbola is a horizontal hyperbola and the standard equation of horizontal hyperbola when center is at origin:
The distance from center to focus is 'c' and here focus is at (-50,0)
So, c= 50
Now if the distance from center to the directrix line is 'd', then
Here the directrix line is given as : x= 2304/50
Thus,
⇒
⇒ a² = 2304
⇒ a = √2304 = 48
For hyperbola, b² = c² - a²
⇒ b² = 50² - 48² (By plugging c=50 and a = 48)
⇒ b² = 2500 - 2304
⇒ b² = 196
⇒ b = √196 = 14
So, the equation of the hyperbola is :
Let be the amount of water that evaporates. At the start, the solution in the tub consists of 2.5 gallons of salt (5% of 50 gallons). After
gallons of water evaporates, we're left with a solution with total volume
gallons, and 8% of this amount should be salt, or
gallons of salt. The amount of salt in the tank before and after evaporation remains unchanged, so
gallons of water need to be evaporated.