Find an equation for the line tangent to the curve at the point defined by the given value of t. also, find the value of d^2y / dx^2 at this point.
x = 3t^2 + 7, y = t^6, t = -1

The tangent line has slope , which we can find using the chain rule:

We have

so that

When , the tangent line has slope 1.

To compute the second derivative , first notice that the first derivative turns out to be a function of . Denote this first derivative by . Then by the chain rule, we find

and at , we get a value of 2/3.

answer: .75 km

step-by-step explanation:

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: