Question

please i need help this is the second time i post this please help and show all the steps and make sure it's correct

her weight grows a arate that is rectly proportional to the concen (a) A calf weighs 55 pounds at b. As we us over the next years, hermated mamum we of 1200 pounds and her current weight of w pounds. Set up and use operation of variables to the Dead the (a) Convert the parametric equations asset.3 and ytanf-2 Into rectangular form and then identify the equation. The instructions do NOT say to 1. weight function wit) (b) Use seperation of variables to solve du usin() with u(O) = -1 dy (15 pts.) 2 put a word in a box (b) Show how calculus can be used on the parametric equations to find the equations of all vertical and horizontal tangent lines. Then use these tangent lines to give a detailed sketch of the equation labeling all key points and the orientation. Use your graph to give domain and range of the equation in interval notation Use the parametric equations to show how to find the slope of any tangent lines to the curve at the point where xa 17.

Answer 1

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८ 550 1200-W [len w sol (a) Wo = 55 pounds dW 2 (1200-w) at du K(1200-W) [ k=cendant dw = JK at in1w-12001 kt Ten (w-12001 - 1n 111451] = -kt fen/w-1200 = -kt 1145 to 1200-W = e-kt [ 12007w 1145 -kt (w = 1200 - 11456 (b du = uusin (²) ulo)=4 du du = fusin (03) du enlul = Susin ( du Put ²=t audo=dt enlul = 1 (sint at 2entul = -cost to U ulo) = -1 N So, putting it :- 21n1-11 = caso + c. c=1 2 enly) = 1 -cost a inlul = 1- cos(62 Hence a o

2. (a) x= 7xect +3 sect = 4 tant ya y = 8 tant - 2 V seat tan't = 1 72 82 This is the eph of a typerbola with centre at (3,2 Hyperbola's gen. eqh = x - x² + y yo 6+ y po Ni N = 2 b) A parametric cune has horizontal tangent whererer dy =o & restical targent when dildt = 0 dy = 8 sect =0 & sect=0 t does not exist Se no horizontal tangert 7sect tant =0 sint =o at cost sint=0 (t = nel So, there are vertical tangents x= 7sect +3 Stant-2 at t=0, x= 10, y = -2 at t=r, x=-4, y = -27 at t=21, x = 10, y = -2 (values repeating at t= -1 , x=10, y = -2 - So, the vertical tangent are (x =-41 & ta = 10

centre of the graph is (3, -2), hyperbola Tertical targets x=-4 &x=10 So the the graph is - ny graph is are 4-3-2-1 1 2 3 4 5 6 7 id - -27 -3 at y=09 t= tant (4) So, x=+C)+3 Domain (-004 u Gooo) Range - (6o, o) dy/at Esect dal doldt 7 seet tant 8 7sint at a=17, 17= 7sect +3 = sect=2 sint = 3 Putting in o Centre Idy = 2x2 (T96-17) FX13 753