We can help you, but we can't answer the question for you since it's important for students to work out the problem by themselves.
Based on the problem, we know that since the sum of ##t_7## and ##t_8## is ##5832## and the sum of ##t_3## and ##t_2## is ##24##, we have
##t_2 + t_3 = 24##...
Did you show the work here? I asked this question because I want to see how you approached this problem.
Other than that, the answer is not ##3.8##. I recommend you start this problem by indicating all available info you have.
You are correct; the answer is ##\frac{bt^3}{3}##. Try integrating ##bt^2##, treating ##b## as the constant, by calculus. Which rule do you need to use to integrate such an expression? This is one of the elementary derivative rules.
You didn't multiply ##e^{-\frac{|t|}{t_c}}## by itself. Instead, the second multiplier misses the negative sign. Check your work carefully and try again evaluating the integral.
Your equations are mostly correct, but you forget the ##t## variable next to ##v_i\sin(35^{\circ})##. That is because the ##y##-component distance formula is ##y(t) = y_0 + v_i\sin(\theta)t + \dfrac{1}{2}gt^2##. Be sure to first express in that form.
If you place an object on the hill at some height ##h##, then it only has a potential energy, which is a total energy. Let it go, so without friction, the moving object, which makes back at a height ##h##, has that amount of potential energy and reaches zero velocity. However, zero velocity at...