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
In the drawing the base picture shows two squares on next to each other
The side picture shows three squares, one next to other and one above the square that right most.
The front picture shows two one square above other square.
The three dimensional figure that corresponds to those three view is a set of three boxes two in the base and one above one of the boxes of the base.
Use elimination.
-x = -6
X = 6
-4 (6) + 4y = 12
Y = 9
(X,y)
(6,9) is the solution
Answer: The Answer is B
Step-by-step explanation:
You need to distribute 15x(10x - 4). 15x times 10x is 150x and since there is 2 x's your gonna square it. So then it would be 150x². next 15x times -4 is -60 and add your x. Your answer is 150x² - 60x.
