Question

Find parametric equations for the curve of intersection of the cylinders x^+y^2=1 and x^2+z^2=1. Use 3D Calc Plotter to graph the two surfaces. Then graph your parametric equations for the curve of intersection. Use a different constant primary color for each of your parametric curves. Print out your graph.

I need help on how to do this using 3D Calc Plotter please.

Thank you.

Answer #1

a) Find a parametric equation for a curve given as an
intersection of a sphere x^2 + y^2 + z^2 = 1 and a plane x + z = 1,
where 0 ≤ a ≤ 1.
b) Do the contour plot of the function f(x, y) = x 2 −y 2 . The
contour plot is a collection of several level curves drawn on the
same picture (be sure to include level curves for positive,
negative and zero value of...

Consider the following planes.
x + y + z = 1, x + 3y + 3z = 1
(a) Find parametric equations for the line of intersection of
the planes. (Use the parameter t.)
(x(t), y(t), z(t)) =
(b) Find the angle between the planes. (Round your answer to one
decimal place.)
°

the curve shown below has parametric equations : x =
t2 - 2t +2, y = t3 - 4t (- infinity <t
< infinity).
find the value of t which gives point (10,0) on the curve, and
determine the slope of the curve at this point.

1)Find sets of parametric equations and symmetric equations of
the line that passes through the two points. (For the line, write
the direction numbers as integers.)
(5, 0, 2), (7, 10, 6)
Find sets of parametric equations.
2) Find a set of parametric equations of the line with the given
characteristics. (Enter your answer as a comma-separated list of
equations in terms of x, y, z, and
t.)
The line passes through the point (2, 1, 4) and is parallel to...

4. Consider the function z = f(x, y) = x^(2) + 4y^(2)
(a) Describe the contour corresponding to z = 1.
(b) Write down the equation of the curve obtained as the
intersection of the graph of z and the plane x = 1.
(c) Write down the equation of the curve obtained as the
intersection of the graph of z and the plane y = 1.
(d) Write down the point of intersection of the curves in (b)
and...

Find the length of the curve defined by the parametric
equations
x=(3/4)t y=3ln((t/4)2−1)
from t=5 to t=7.

Use Lagrange multipliers to find the highest point on the curve
of intersection of the surfaces.
Sphere: x2 + y2 + z2 =
24, Plane: 2x + y − z = 2

Consider the surfaces x^2 + y^2 + z^2 = 1 and (z +√2)^2 = x^2 +
y^2, and let (x0, y0, z0) be a point
in their intersection. Show that the surfaces are tangent at this
point, that is, show that they
have a common tangent plane at (x0, y0, z0).

Using MatLab
2. Given the parametric equations x = t^3 - 3t, y = t^2-3:
(a) Find the points where the tangent line is horizontal or
vertical (indicate which in a text line)
(b) Plot the curve parametrized by these equations to
confirm.
(c) Note that the curve crosses itself at the origin. Find the
equation of both tangent lines.
(d) Find the length of the loop in the graph and the area
enclosed by the loop.
3. Use what...

Find the derivative of the parametric curve x=2t-3t2,
y=cos(3t) for 0 ≤ ? ≤ 2?.
Find the values for t where the tangent lines are horizontal on
the parametric curve. For the horizontal tangent lines, you do not
need to find the (x,y) pairs for these values of t.
Find the values for t where the tangent lines are vertical on
the parametric curve. For these values of t find the coordinates of
the points on the parametric curve.

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