The curve given by the parametric equations;
x=36−t^2, y=t^3−25t
is symmetric about the x-axis. (if t gives us the point (x, y), then −t will give (x,−y) ).
a. at which x value is the tangent to this curve horizontal?
b. at which t value is the tangent to this curve vertical?

x=36, t = ±5/sqrt 3

Step-by-step explanation:

we are given a curve reprsented by parametric equations.

Also given that this is symmetric about x axis.

For finding a tangent we first find slope i.e. dy/dx

If dy/dx has dy/dt in numerator and dx/dt in the denominator

Hence for a tangent to be horizontal slope =0

i.e.dy/dt =0

Similarly for a tangent to be vertical slope=undefined

Or dx/dt =0

a)

when x= 36, the tangent is horizontal

b)

For these t values tangent is vertical.

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

his chances of getting a coin of higher value is 4/19

step-by-step explanation: