When converting polar to rectangular, rsin(theta) gives this coordinate.
What is y?
100
The third variable, often time, used to create this style of equations is called this...
What is the parameter?
100
Write <3,4> as a sum of scalars of the standard unit vectors.
What is 3i + 4j?
100
For a position vector r(t) = <3t^2, 5 - t^3>, what is the velocity vector at t = 1?
What is <6, -3>?
100
Write the integral that represents the arc length of a parametric equation given x = f(t) and y = g(t) for a smooth curve C on the interval a < t < b.
What is integral from a to b of the SQRT((f'(t))^2 + (g'(t))^2) dt?
200
When converting polar to rectangular, rcos(theta) gives this coordinate.
What is x?
200
The (x,y) coordinate when t = 3 for this graph:
x(t) = 2t y(t) = t^2
What is (4,9)?
200
Write r(t) = < a, b, c > as the sum of scalars of unit vectors in 3-D.
What is ai + bj + ck?
200
For the position vector r(t) = <3t^2, 5 - t^3>, what is the acceleration vector at t = 1?
What is <6, -6>?
200
Write the formula that represents the arc length of a polar equation given r = f(theta) for a smooth curve C on the interval a < theta < b.
What is integral from a to b of SQRT (r^2 + (dr/d(theta))^2) d(theta)?
300
The graph of r = 4
What is a circle with radius 4
300
Simplify dy/dt / dx/dt
What is dy/dx?
300
When v = <3, 4>, then SQRT (3^2 + 4^2) represents the _____________ of the vector.
What is magnitude?
300
For the particle with velocity vector <5t, t - 1>, find the speed of the particle at t = 4.
What is SQRT (409) or 20.224.
300
Find the area of one petal of the rose created by r = 3cos(3theta) from theta = -pi/6 to pi/6.
What is 3pi/4?
400
The graph of theta = pi/4
What is a diagonal line through the first and third quadrants, equivalent to y = x.
400
Simplify d[ dy/dt / dx/dt]/dt / dx/dt
What is d^2y / dx^2
400
When v = <3,4> then tan^-1 (4/3) represents the ________ of the vector.
What is direction?
400
The position of a particle is given by x(t) = t^2 - 5 and y(t) = 4/3t^3 for t>=0. Find the magnitude of the velocity vector at t = 2.
What is 4*SQRT(17) or 16.492
400
Use fnInt to find the area of the surface of revolution when the curve formed by the parametric equations x=3cos(t) and y = 3sin(t) from 0
What is 9pi?
500
The name of a polar graph created by an equation such as r = 5(1-cos(theta))
What is a cardiod?
500
The name of the curve formed by parametric equations of the form:
x = r(theta - sin(theta)) and y = r(1 - cos(theta))
What is a cycloid?
500
If v(t) = <4t^2, t^3 - 6t>, then v'(t) = ?
What is <8t, 3t^2 - 6>?
500
Using your graphing calculator, graph the polar equation r = 3 - 6cos(theta) and use the Draw Tangent option at theta = pi/2 to find the slope of the tangent line there.
What is -2
500
Find the arc length for the curve between the points (1,1) and (4,8) on the graph of x(t) = t^2 and y(t) = t^3. Use fnInt to evaluate. (Hint, find interval for t between the given points first.)