solve the follwing and show working

Differentiation Applications 1: Related Rates A 10 lodder is leaning against a wal when the bottom begins to sip out. Assume that the arrow on each dirhwing At any moment, the bottom of the ladder is x feet from the wall, and the top or the la What is the veloelty of the top of the ladder when it is a given distance above the ground? Construct Your Understanding Questions (to do in class) 1. Label the distances x and y in the first and last drawings in Model 1 . 2. When.. a. y=8f, what is x ? b. y=3f, what is x ? White down any equations you used to find your answers. 3. Suppose we want to know the velocity of the 100 of the ladder when y=8 feet. A good way to begin answering this question is to take an inventory of what is known and unknown, assigning variables to each. Do this by completing the table below. (Check your work) There should be enty one unknown in the tabie in Model 4 , and this should correspond to the chould be enty one unknown in ine tabis in in Model 1 . If you listed a value of " p tor both velocities. read Model 4 more carefully and change one of these to an actual value. 5. Note that x and y in Modet 1 are changing with time (t), so each is a function of t. a Construct a deschption of what these symbols mean in the context of Model 4 i. dirdis ki. dtsy b. (Check your work) If you have not already done so. circle x or y in the last two rows on the table in Question 3 Write dtdx and dxdy in the appropriate boxes of the table, and check that your descriptions above match the descriptions in the tabie. c. Is difAy positive or negative? Circle one, and explain your reasoning d. (Check your work) is your answer to part c consistent with the fact that dittr and dtdy have opposite signs in this problem? 6. (Check your work) Did you cite the equation x2+y2=100 in Question 2 ? a. If not, go back and check your work. b. Starting from this equation, use implicit differentiation to generate an expression for dtdy, in terms of the variables and rates of change on the table in Model 1. (If you are stuck, move onto parts c-e on the next page.)