Answer:
Step-by-step explanation:
C=2*3.14*r
radius, r=11.5
C=72.22 cm
<u>Answer</u>
a. r^n=a
c.^n√a=r
<u>Explanation</u>
<u><em>solution 1</em></u>
a⁽¹/ⁿ⁾ = r
Powering both sides of the equation by n;
a⁽¹/ⁿ ₓ ⁿ⁾ = rⁿ
<em>a¹ = rⁿ </em>
<u><em>solution 2</em></u>
Also,
a⁽¹/ⁿ⁾ = r
a⁽¹/ⁿ⁾ = ⁿ√a <em> (nth root of a)</em>
<em>ⁿ√a = r</em>
A)
to solve a, the following rules are crucial:
(i)
so the difference of 2 logarithms with the same base, is the logarithm of their division, preserving the same base.
(ii) if
then b=c.
so if 2 logarithms with the same base are equal, then the arguments (b and c) are equal as well.
so
apply rule (i):
apply rule (ii):
now 'isolate' y:
b)
some more rules:
(iii)
(iv)
apply iii and iv:
then substitute
in the equation:
so now we have a quadratic equation of degree 2,
a=2, b=-5, c=2
the discriminant is
, the root of it is 3
so the roots are:
and
finally, we convert u's to x's:
means
so for u=2, x=4, and for u=1/2 we have x=1/4
Answers:
A) y=(6 x^{2} -1) \frac{(x-1)}{x}
B) solution set: {4, 1/4}