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Practice Test 1 - Math 2401— Midterm I Page 1[1 The area...

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Unformatted text preview: Math 2401— Midterm I Page 1 [1] The area of a triangle is given by the formula , 1 \ At time to, be : 10 inches, co = 15 inches and (90 = 7r/3 radians. (a) Find the area of the triangle at time to. (b) Find the rate of change of the area with respect to b at time to given that c and 0 remain constant. 3 A ,_, aging ._¢ 2 35 112A}? (c) Find the rate of change of the area with respect to 6 at time to given that b and 0 remain constant. (9A - —(’ LL)(’°SG 776 L] (e) Find the rate of change of c With respect to b at time to given that the area and «9 remain constant. A ‘ 1? 5.4.0 C:-(\ei gme 4 a: a); (2L. 9» '" sue 1 51 Math 2401* Midterm I Page 2 [2] The curvature H of a plane curve F(t) is given by H = I$’(t)y”(t) — l’L‘”(t)y’(t)l ($1732 + y’(t)2)‘°’/2 Compute the curvature of the curve 33 2 fight + 1) at x : 2. Ha: (xla ,le HQ: (J6) \nItHfi . * % {m , {M2 \ ' yM: w ‘ /~ » ‘3 ’ $ -1 -\ r M: 0 7M ‘2 W 0‘ “’ WI)?" Math 2401— Midterm I Page 3 [3] (a) Show that the curve fit) = (252 —~ 25 + 1)?+ (t3 — t + 2)j+ $11ng ‘ \ intersects itself at a unique point P With Whose third coordinate is zero. ‘ W" ( Z : 9“" U}:£\ '6 Q“; ‘ (13 711’ -v {7 ” KM (03 _ O) 1 7‘0 , 7; A (03 L0 0 “\A +(O *Otlm Main”) fm’ (I “PM; 4* (334 *2): A { A “A“ ”L ¥ 1“) L 0}: mm)? +14 cum Mamas mdé ) N'Hni X’W‘t U 7 IO) (b) Find theu nit tangeht memf'fhe curve fl): J'%‘ A WM: (“Us 4311 V+(3t1;~1)3‘+ Reodfl)? Math 2401— Midterm I ' Pa e 4 [4] A bee moves out of the hive along a curve C in such a manner that its velocity is always twice its position vector. The position of the hive is at the point (1, 2, 1). (a) Find parametric equations of C. m a ‘m “M : *2 v) “8:211“ 3 KN) :nez: Klalfl like l:o\ 7m - 1 W3 3 7m :te” «up, Tim > 1E) 1‘05 WMszmmsa ,, ‘q ‘ ~ " “1W MW WW (b) Find the position of the bee at t— —— 1 M” M ,_ » WNW-WM *W' Mhmwms. WNW ”M WWW» NMWWW ‘\ : (sill/t: +(Zt7'y3‘ rang—um, ...
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