Answer:
C
Step-by-step explanation:
Answer:
x = 1 - 5t
y = t
z = 1 - 5t
Step-by-step explanation:
For the equation of a line, we need a point and a direction vector. We are given a point (1, 0, 1).
Since the line is suppose to be a tangent to the given curve at the point (1, 0, 1), we need to find a tangent vector for which the curve passes through that point.
We have x = e^(-5t)cos5t
at t = 1, x = e^(-5)cos5
at t = 0, x = 1
y = e^(-5t)sin5t
at t = 1, y = e^(-5)sin5
at t = 0, y = 0
z = e^(-5t)
at t = 1, z = e^(-5)
at t = 0, z = 1
Clearly, the only parameter value for which the curve passes through the point (1, 0, 1) is t = 0.
In vector notation, the curve
r(t) = xi + yj + zk
= e^(-5t)cos5t i + e^(-5t)sin5t j + e^(-5t) k
r'(t) = [-5e^(-5t)cos5t - e^(-5t)sin5t] i +[e^(-5t)cos5t - 5e^(-5t)sin5t] j - 5e^(-5t) k
r'(0) = -5i + j - 5k
is a vector tangent at the point.
We get the parametric equation from this.
x = x(0) + tx'(0)
= 1 - 5t
y = y(0) + ty'(0)
= t
z = z(0) + tz'(0)
= 1 - 5t
Answer:
The answers below ._.
Step-by-step explanation:
A secant is a line that intersects a circle in exactly two points. When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
Answer:
The number of students who liked the book was 64.
Step-by-step explanation:
After reading a book for English class, 100 students were asked whether or not they enjoyed it.
Now, given that nine twenty-fifths of the class did not like the book.
So, 
of the whole class did not like the book.
Then, the fraction of the class who did like the book was 
.
Therefore, the number of students who liked the book was 
. (Answer)
