Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2 sin(t)i + 7 cos(t)j t = π/6

Applying derivatives, the tangent vector of unit length at the point given is:

The vector function is:

The tangent vector is it's derivative, which is given by:

At point , we have that:

The norm of the vector is:

The unit vector is given by each component divided by the norm, thus:

A similar problem is given at link

The tangent vector to r(t) at any t in the domain is

At t = π/6, the tanget vector is

To get the unit tangent, normalize this vector by dividing it by its magnitude:

So the unit tangent at the given point is

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

ask the math teacher she or he would know lol.

step-by-step explanation: