Step-by-step explanation:

Let the curve C be the intersection of the cylinder
and the plane
The projection of C on to the x-y plane is the ellipse
To see clearly that this is an ellipse, le us divide through by 16, to get
or
,
We can write the following parametric equations,
for
Since C lies on the plane,
it must satisfy its equation.
Let us make z the subject first,
This implies that,
We can now write the vector equation of C, to obtain,
The length of the curve of the intersection of the cylinder and the plane is now given by,
But
Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.
Answer:
32 one-dollar bills.
Step-by-step explanation:
Let <em>x </em>represent one-dollar bills and <em>y </em>represent two-dollar bills.
He has a total of 49 bills. Therefore:

The total amount of money James has is 66. <em>x</em> is worth one dollar, while <em>y</em> is worth two dollars. Therefore:

We have a system of equations. Solve by substitution:

Therefore, James has 32 one-dollar bills and 17 two-dollar bills.
Checking:

Answer:
Step-by-step explanation:
Go on super teacher worksheets to get the answer key