r(t) = (x(t), y(t), z(t)) where ¤(t) = y(t) z(t) = – 5t? – 4t2 – 5t – 3 5t? + 5t + 3 Since all components are of no higher degree than quadratic, r'''(t) torsion of this curve is zero. This means the binormal vector B = B(t) is constant, and that the curve lies in a single plane. < 0, 0, 0 > and so the a) Find the equation of this plane. You may enter an equation like a(x – xo) + b(y – y) + c(z – zo) = 0 or an equivalent expression.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
This is a calculus 3 problem. Please explain each step clearly, no cursive writing.
![The function \( r(t) = \langle x(t), y(t), z(t) \rangle \) is defined as follows:
\[
x(t) = -4t^2 - 5t - 3
\]
\[
y(t) = 5t^2 + 5t + 3
\]
\[
z(t) = -5t^2
\]
All components are quadratic, thus the third derivative \( r'''(t) = \langle 0, 0, 0 \rangle \), making the torsion of the curve zero. This indicates that the binormal vector \( B = B(t) \) is constant, and the curve lies in a single plane.
**Task:**
a) Determine the equation of this plane.
An equation can be entered in the form:
\[
a(x - x_0) + b(y - y_0) + c(z - z_0) = 0
\]
or an equivalent expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb9da028-c1e8-4fb4-9df2-7f4287e8030e%2F738629c6-1dfc-484e-a1be-44219a335491%2F2n6sjz06_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
