V(t) = πr^2h
V'(t) = π(2rr'h + r^2h')
V'(t) = π(2(5)(-2)(7) + 5^2(8)
V'(t) = π(-140 + 200)
V'(t) = 60π in^3
The intersection can be parameterized by
with
.
By Stoke's theorem, the integral of
along
is equivalent to
where
is the region bounded by
. The line integral reduces to
Hello from MrBillDoesMath!
Answer: 1/2
Discussion:
Note that:
16 /2 = 8 (the next term in the sequence)
8 /2 = 4 (the next term in the sequence)
4 /2 = 2 (the next term in the sequence)
We are repeatedly multiplying by 1/2
Thank you,
MrB
A recursive sequence is a sequence of numbers whose values are determined by the numbers that come before them in the sequence.
We’re given a sequence whose (n + 1)-th term f(n + 1) depends on the value of the n-th term f(n), specified by the recursive rule
f(n + 1) = -4 f(n) + 3
We’re also given the 1st term in the sequence, f(1) = 1. Using this value and the recursive rule, we can find the next term f(2). (Just replace n with 1.)
f(1 + 1) = -4 f(1) + 3
f(2) = -4 • 1 + 3
f(2) = -1
We do the same thing to find the next term f(3) :
f(2 + 1) = -4 f(2) + 3
f(3) = -4 • (-1) + 3
f(3) = 7
One more time to find the next term f(4) :
f(3 + 1) = -4 f(3) + 3
f(4) = -4 • 7 + 3
f(4) = -25
