Find the parametric equations and the symmetric equations for the line. The line of intersection of the planes x + 2y +3z = 1 and x - y + z = 1. Please explain...

Find the parametric equations and the symmetric equations for the line. The line of intersection of the planes x + 2y +3z = 1 and x - y + z = 1. Please explain...

At what points does the curve r(t) = ti + (4t − t^2)k intersect the paraboloid z = x^2 + y^2? (If an answer does not exist, enter DNE.) smaller t-value (x, y, z) =...

Convert the following parametric equations to a rectangular equation: x=2cos2t y=2sin2t ...

A.) 14-3x B.) x+4 C.) 3x+2 D.) 4-x

A comet following a hyperbolic path about the sun has a perihelion of 140 Gm. When the line from the comet to the Sun is perpendicular to the focal axis of the orbit, the comet is 405 Gm from the...

An amusement park designs a roller-coaster ride based on the function f(t)=at^2-bt+20, where t is the time of the ride in seconds. The designer wants to achieve the speed f'(1)=10 mph, and f'(15)=80...

convert the following parametric equations into a rectangular equation x=-2sinT y=2cosT

1. Describe the components of the vector v(t)=<t2,5t> and the meaning of this vector. 2. Convert the following parametric equation into a rectangular equation: {x(t)=5cost}...

Evaluate the following integral using any Vector Calculus method The integral with bounds C; [(4+eyz)i+(xzeyz+2yz)j+(6z2+xyeyz+y2)k] dot dr, where C is the part of...

How to eliminate the parameter given the following equations: x=(cos(x))^2 y=(cos(x))^4 + 2 I would understand if it was just plain old sine and cosine that you could square...

Find a rectangulat equation for this parametric equation x=1/t y=3

(Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) 1)once around clockwise, starting at (4,3) 0≤t≤2pi 2)three times around counter clockwise,...

(problem continued)..."and P2(x2,y2). Draw the triangle with vertices A(1, 1), B(4, 3), C(1, 7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated...

Please help me! I have no glue on how to answer this question, and my teacher did not explain it very well

1) x=3-2t y=2+3t 2) x=sqrt(t) y=1-t 3) x=4+2cos(theta) y=1+2sin(theta) 4)...

The equations x + 3 x^{3/2} = t^2 + t and y\sqrt{t+1}+2t\sqrt{y} = 2 define x and y implicitly as differentiable functions x=f(t) and y=g(t). Find the slope of the curve x=f(t), y=g(t)...

Write the rectangular form for the parametric equation x=cosθ ; y=4sinθ

Eliminate the parameter x=4+2 cos∅ y=1+2 sin∅ I think i can solve it like this but i am not sure x=4+2cos∅ x-2=4cos∅ x-2/4=cos∅

I understand parametric equations for the most part, but i always have trouble with finding their intersection points. I would be glad for a second opinion. Thanks so much!

I have the answers {x=2t, y=(1/8t^3) } and {x=t, y=(1/t^3)} If I have the wrong answers could you explain how to get the right ones? I have to answer this in class tomorrow and I'm insanely paranoid...