Are 3.25/2.5 , 5.98/4.6 and 6.76/5.2 proportional?
2 answers:
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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 :
The radius of the cylinder is 2.92 cm
<u>Explanation:</u>
Given:
Volume of cylinder, V = 193 cm³
Height of the cylinder, h = 7.2 cm
Radius of the cylinder, r = ?
We know:
Volume of cylinder = πr²h
On substituting the value we get:
Therefore, the radius of the cylinder is 2.92 cm