Answer:
82.1
Step-by-step explanation:
Multiply each grade by its weighted percentage, then add up the results.
Answer:
The torsion of the helix is .
Step-by-step explanation:
To complete this exercise we need to recall the formula for the torsion of a curve. Given a parametrization the torsion of the curve is given by
.
So, the first step is to find the derivatives of the vector function .
Thus,
,
,
,
.
Now, we must calculate the cross product of the vector functions and .
.
Now we calculate :
Recall that the norm of a vector in the space is
.
At this point we have
.
Splitting up the interval of integration into subintervals gives the partition
Each subinterval has length . The right endpoints of each subinterval follow the sequence
with . Then the left-endpoint Riemann sum that approximates the definite integral is
and taking the limit as gives the area exactly. We have
The altitude of the rectangle ?