If r = 12 cm, what is the area of this sector? Express your answer to the nearest tenth of a centimeter.
2 answers:
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Answer:
a) The horizontal asymptote is y = 0
The y-intercept is (0, 9)
b) The horizontal asymptote is y = 0
The y-intercept is (0, 5)
c) The horizontal asymptote is y = 3
The y-intercept is (0, 4)
d) The horizontal asymptote is y = 3
The y-intercept is (0, 4)
e) The horizontal asymptote is y = -1
The y-intercept is (0, 7)
The x-intercept is (-3, 0)
f) The asymptote is y = 2
The y-intercept is (0, 6)
Step-by-step explanation:
a) f(x) =
The asymptote is given as x → -∞, f(x) = → 0
∴ The horizontal asymptote is f(x) = y = 0
The y-intercept is given when x = 0, we get;
f(x) = = 9
The y-intercept is f(x) = (0, 9)
b) f(x) =
The asymptote is fx) = 0 as x → ∞
The asymptote is y = 0
Similar to question (1) above, the y-intercept is f(x) = = 5
The y-intercept is (0, 5)
c) f(x) = 3ˣ + 3
The asymptote is 3ˣ → 0 and f(x) → 3 as x → ∞
The asymptote is y = 3
The y-intercept is f(x) = 3⁰ + 3= 4
The y-intercept is (0, 4)
d) f(x) = 6⁻ˣ + 3
The asymptote is 6⁻ˣ → 0 and f(x) → 3 as x → ∞
The horizontal asymptote is y = 3
The y-intercept is f(x) = 6⁻⁰ + 3 = 4
The y-intercept is (0, 4)
e) f(x) = - 1
The asymptote is → 0 and f(x) → -1 as x → -∞
The horizontal asymptote is y = -1
The y-intercept is f(x) = - 1 = 7
The y-intercept is (0, 7)
When f(x) = 0, - 1 = 0
= 1
x + 3 = 0, x = -3
The x-intercept is (-3, 0)
f)
The asymptote is → 0 and f(x) → 2 as x → ∞
The asymptote is y = 2
The y-intercept is f(x) =
The y-intercept is (0, 6)
SOLUTION
We have been given the equation of the decay as
So we are looking for the time
Plugging the values into the equation, we have
Taking Ln of both sides, we have
Hence the answer is 4308 to the nearest year
The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted , which we can parameterize by the vector-valued function,
for , which has differential
Then with , we have
Complete the square in the quadratic term of the integrand: , then in the integral we substitute
:
Make another substitution of :
Integrate by parts, taking
So, we have by the fundamental theorem of calculus that