Amy is riding a Ferris wheel at a carnival. After a time $t$, her height $H$ above the ground is given by the following formula. \[ H=a \cos (b t)+c \] Find Amy's height above the ground when $a=-35 \mathrm{~m}, b=0.82 \mathrm{rad} / \mathrm{s}, t=7 \mathrm{~s}$, and $c=47 \mathrm{~m}$. Do not round any intermediate computations. Round your answer to the nearest hundredth. \[ H=\square \mathrm{m} \]

Step 1 ：The problem provides us with the formula for Amy's height above the ground after a certain time, which is given by \(H=a \cos (b t)+c\).

Step 2 ：We are given the values of \(a=-35\) meters, \(b=0.82\) radians per second, \(t=7\) seconds, and \(c=47\) meters.

Step 3 ：We substitute these values into the formula to find the height: \(H=-35 \cos (0.82 \times 7)+47\).

Step 4 ：After calculating, we find that \(H=17.03766718569608\) meters.

Step 5 ：Rounding this to the nearest hundredth, we get \(H=17.04\) meters.

Step 6 ：Final Answer: The height of Amy above the ground at time \(t=7\) seconds is \(\boxed{17.04}\) meters.