Answer:
x² + y² = 6.25
Step-by-step explanation:
The standard equation of a circle is ( x – h)² + ( y - k)² = r² where the center is (h, k) and r is the radius.
From your given information that the center is (0, 0) then both h and k are 0. Then r is 2.5, so
( x – 0)² + ( y - 0)² = (2.5)²
x² + y² = (2.5)²
x² + y² = 6.25
f(x)=lnx
y=f(x)
dy/dx= 1/x
tangent at (x,y) has slope 1/x
eqn of tangent is y = mx + c
since the tangent passes through origin, c=0
substitute y = lnx and m= 1/x to above eqn
lnx = 1
x=e
y=lne=1
Apply the radical rule to separate terms:
Cubicroot(-27) and cubic root(n^27)
Cubicroot(-27) = -3
Now you have -3 cubicroot(n^27)
Using the exponent rule
N^27 can be rewritten as (n^9)^3
Now you have -3 cubicroot((n^9)^3)
The cubic root and the 3rd power cancel out to get the final answer of
-3n^9
See attached picture for the answers:
