Xy + 6e^y = 6e
taking first derivative :
<span>xy' + y + 6y(e^y)(y') = 0 </span>
<span>xy" + y' + y' + 6y'(e^y)(y') + 6yy(e^y)y' + 6y(e^y)y" = 0 </span>
<span>Put x = 0,
0 + 6e^y = 6e,
y = 1 </span>
<span>0 + 1 + 6(1)(y')e = 0,
Put y' = 0 </span>
<span>0 + 0 + 0 + 0 + 0 +6 ey" = 0,
y" = 0</span>
Given:
.
To find:
The value of x.
Solution:
In triangles ABC and ADE,
(Right angles)
(Common angles)
(AA property of similarity)
We know that the corresponding sides of similar triangles are proportional. So,




On cross multiplication, we get



Therefore, the value of x is
units.
Answer:
-2/3 gal per minute
Step-by-step explanation:
The pool drained 4 gallons in 6 minutes.
How many gallons per minute?
minutes: 6 min/6 = 1
gallons: 4 gal/6 = 2/3
-2/3 gal per minute (negative because the pool is draining)
Answer:
8483 ft²
Step-by-step explanation:
Subtract the area of the smaller circle from the area of the greater circle
Greater Circle area:
πr² = π × 140²
= 61583.2 ft²
Smaller Circle area:
= π × 130²
= 53099.8 ft²
Area of track:
61583.2 - 53099.8 = 8483.4ft²
= 8483ft² (to the nearest ft²)