Answer :
Let's assume the opposite of the statement i.e., 3 + √5 is a rational number.
Since, a, b and 3 are integers. So,
Here, it contradicts that √5 is an irrational number.
because of the wrong assumption that 3 + √5 is a rational number.
Hence, 3 + √5 is an irrational number.
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 :
Answer:
Step-by-step explanation:
1) 2y + 6x
2) 2y + 8x +2
-160=22+8(3p-4)
Use distributive property
-160=22+24p-32
-160=24p-10
Add 10 for both side
-160+10=24p-10+10
-150=24p
Divided 24 for both side
-150/24=24p/24
p=-6.25
Check:
-160=22+8(3p+4)
-160=22+8[3(-6.25)-4]
-160=22+8(-18.75-4)
-160=22+8(-22.75)
-160=22-182
-160=-160. As a result, x=-6.25. Hope it help!