Calculus Answers

Using a table, sketch the parametric equations, including the orientation arrows. 

x = t² - 2t

y= -t² + 4t

0 ≤ t ≤ 3

A particle moves in the xy-plane with the position given by the parametric equations:

x = t³ - t² - 9t +9

y = 2 - t

Find the location of the particle when t = 1.

(_, _)

Let C be the curve defined by the parametric equations:

x = 4t² + 4t

y = 2cos(t) + 3

t ∈ [0,π]

a) Find the value of t on the indicated domain when the x-coordinate of the curve is 3. Write your answer as a fraction

t =

b) Find the value of t on the indicated domain when the y-coordinate of the curve is 2. Round your answer to 3 decimal places 

t =

c) Find the y-intercept of the curve.

The y-intercept is at ( 0,_)

Which graph represents the parametric equations 

x = t – 4

y = t² + 5

–1 ≤ t ≤ 2

Using a table, sketch the parametric equations, including the orientation arrows.

x = t^2 -2t

y = -t² + 4t

0 ≤ t ≤ 3

A particle moves in the xy-plane with the position given by the parametric equations:

x = t^3-t^2-9t +9

y = 2-t

Find the location of the particle when t = 1.

(_,_)

the mass of the polar ice caps is modeled as a function of time, call it m(t). if scientists discover that the polar ice caps are still melting more and more each year, what are the signs of the first and second derivatives of m(t)?

The top of a 23 feet ladder, leaning against a vertical wall is slipping down the wall at a rate of 3 feet per second. How fast is the bottom of the ladder slipping along the ground when the bottom of the ladder is 10 feet away from the base of the wall?

starting from the same point, Biden starts walking eastward at 52 m/s while Trump starts running towards the south at 86 m/s. How fast is the distance between Biden and Trump increasing after 2 seconds? (Input your final answer on the box below without units of measure

Find the directional derivative of the function at P in the direction of v. f(x, y) =

x/y P(1,1) v = −j