The slope of that equation is (1/3)x. To find the perpendicular slope of a slope, you would have to find the reciprocal. To do this:
Flip the slope, and add a negative. It'll equal to -3x. Visual representation:
https://puu.sh/zPz5u/85fcdde6ab.png
now the perpendicular slope is -3, you will need to put this into point slope form, which is y - y1 = m(x - x1)
x1 = 5, y1 = -3
It'll equal to: y + 3 = -3(x - 5)
Now, you need to convert this to slope intercept form y = mx + b. All you need to do is just to distribute the -3 in that binomial, and move that 3 in the left side to the right side. It is easy!
Follow the representation, and there you go!
https://puu.sh/zPzak/d3ee776f3d.png
For question number 1:The plot H = H(t) is the parabola and it reaches its maximum in the moment when exactly at midpoint between the roots t = 0 and t = 23. At that moment t = 23/2 or 11.5 seconds.
For question number 2:To find the maximal height, just simply substitute t = 11.5 into the quadratic equation. The answer would be 22.9.
For question number 3:H(t) = 0, or, which is the same as -16t^2 + 368t = 0.Factor the left side to get -16*t*(t - 23) = 0.t = 0, relates to the very start of the process, when the ash started its way up.The other root is t = 23 seconds, and it is precisely the time moment when the bit of ash will go back to the ground.
14 fourths, because since 4 fourths make up 1, we would multiply 4 times 4, which gives us 16, and then add the extra 1/4. =)
I believe its 116,464 km?