Find T, N, and B for the curve at the indicated point. [HINT: After finding T', plug in the specific value for t before computing N and B.] r(t) = t, t, et at (0, 0, 1)

Step-by-step explanation:

Given that

To find tangent, normal and binormal vectors at (0,0,1)

i) Tangent vector

At the particular point, r'(t) = (1,1,e)

Tangent vector =

ii) Normal vector

T'(t) =

At that point T'(t) = (0,0,e)/e = (0,0,1)

iii) Binormal

B(t) = TX N

=

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.