I am good at science. Why do you ask?
:)
Well, by definition, the tangent vector is the vector that is the result of differentiating every component of the function. Hence, the tangent vector is T=(3,-5sint,5cost). This has a magnitude of
which yields |r|=
(by using the known trigonometric formula
that holds for all t). Thus, the unit tangent vector t is given by: t=
. Now, to find a normal unit vector, we just need to find a normal vector N and scale it appropriately. To find a normal unit vector, we can just find vector that satisfies V*T=0 (dot product of vectors). By inspection, we see that the vector N=(0, cost, sint) satisfies this requirement and that it is also a unit vector (due to the aforementioned trigonometric identity). Hence, a normal unit vector to our vector function is N.
Answer:
3x^2 - 36x + 108
Step-by-step explanation:
U have a geometric sequence. To find the common ratio, divide the second term by the first term. 6/12 = 1/2
an = a1 * r^(n-1)
n = term to find = 10
a1 = first term = 12
r = common ratio = 1/2
now we sub
a(10) = 12 * 1/2(10 - 1)
a(10) = 12 * 1/2^9
a(10) = 12 * 1/512
a(10) = 12/512 reduces to 3/128 ,<== ur 10th term
r + 32 ≥ 56
Subtract 32 from both sides
r + 32 - 32 ≥ 56 - 32
r ≥ 24