Question

Need all parts for each please and thanks

On the moon, all free-fall distance functions are of the form s(t) 0.81t2, where t is sec, consider parts (a) through (d) below. seconds and s is in meters. An object is dropped from a height of 200 meters above the moon. After a) How far has the object fallen? b) How fast is it traveling? c) What is its acceleration? d) Explain the meaning of the second derivative of this free-fall function a) The object has fallenm. (Type an integer or decimal rounded to two decimal places as needed.) 2000t The function p(t)=4t +75 models the population p of deer in an area after t months. a) Find p'(17), p'(85), and p'(170). b) Find p''(17), p'(85), and p"(170). c) Interpret the meaning of your answers to part (a) and (b). What is happening to the population of deer in the long term? a) p'(17) (Type an integer or decimal rounded to three decimal places as needed.) thousands of dollars, after t months of marketing a product is given by S(t)=3t5 - t+6t-6. Find S'(2) and S"(2). A company determines that monthly sales S, S'(2) (Simplify your answer.)

Answer 1

After t = 6sec (al) O I X3 6 29. (6 m (bD ds OQ X 2t cdt B1 162 t 2 = i 62 X 6 = 97 2 m acceleration tE 1.62 d t dt SRO Z 71.62 (d The re cond dervative givas acceleration 2 o0 t 4t+ 75 2v0 dt 4t475 1tt75)(2u t) -2ntut 75 2000 HtT75 44475

(1 (44+75)2 2 uX75 2 ouuK 75 (4x17 +752 143 22 7 33 5 20r0x75 (4x85+ o. 26 3 a263(5 b) 2 onoK5 clt (4t+75) -2-1 20u0 KSX4X2 200X75 -2( 4t+75) 4tts)3 6OUD00K 2 -1 20000D. (4t ut 410 Þ"(652 0003 The first dori'vative ge the at of in crr0are a pobulctbn The second deivotive with whuch tha rata of tells the rats Inureane is plecreasin n tong +0rm the Iota of inceaae becanme

laosarr SCt =3t3 -t2-t6t-6 Lt 9t- 2tt6 t-18t -2 '12)= 9x 22 -2x2-t 6 3 6-4t6-38 t) x4-2 Herre the fmuta fr dertvati vo are d n ntn- dt fle) dtgit) 2 (ct)