An object is moving in the plane according to these parametric equations:

x(t) = πt + cos(4πt + π/2)
y(t) = sin(4πt + π/2)

the slope of the tangent line to the path at time t is

4πcos(4πt + π/2) divided by (π-4πsin(4πt+π/2))

the first time the tangent line is vertical will be t = ?

the second time the tangent line is vertical will be t = ?

If your annual gross income is $62,000 and you have one monthly car payment of $335 and a monthly student loan payment of $225, what is the maximum house payment you can afford. consider a standard 28% front-end ratio and a 36% back-end ratio. also, to complete your calculation, the annual property tax will be $3,600 and the annual homeowner's premium will be $360.

Terri makes a quilt using three sizes of fabric squares the side lenght of each fabric square is the square root of the area

Follow these steps using the algebra tiles to solve the equation −5x + (−2) = −2x + 4. 1. add 5 positive x-tiles to both sides and create zero pairs. 2. add 4 negative unit tiles to both sides and create zero pairs. 3. divide the unit tiles evenly among the x-tiles. x =