Question

Find two positive numbers such that the sum of twice the first number and three times the second number is 204 and the product is a maximum first number second number Submit Answer MY NOTES ASK YOUR TEACHER [-/1 Points] DETAILS LARCALC11 3.R.080 Find the point on the graph of Rx) - Vå that is closest to the point (6,0). k.no (1 MY NOTES ASK YOUR TEACHER [-/1 Points) DETAILS LARCALC11 3.R.081. A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). What dimensions should be used so that the enclosed area will be a maximum?

Answer 1

bete 221 + 3x2 = 204 8.1) 2x+3y 2 20h 2 first No. y second No. 92 204-22 3 Now и у is maximum N ZA 2 22. ny 2 204-20 3 + 204 3 3 This is an inverted parabula, So its vestex 13 the maximum The X - Cardinale of Vertex 13 - 204 16) zoh a 51 2z -b 4 za 2 (-22) zon- zut) 20h - 2n 3 34 2014 3 اک first Number Second Number : 34 --

9.2) CH,9,) - (@,0) Plu) za y a Ja and (m2, Yz) Distance between two point (ny) is gilum by De (92-y,) & (22 - 2,)? dz Now x2 = 2 922 Ja (50-o)2 + (2-6)2 a tn n² 12ut 36 2 2 71 -11n +36 For minimum distamee. derivation of D should o dD dri d/m² 11 nef36 Z dD dn (2x-11) 2 (x2-11% +369/2 22-U 2 Ju2412+36 22-11 20 22 l 2 ya a la = 2.34 207 (m, y) (5.5 , 2.3452

५ + y PI P2 y 2 Perimeter of ranchor = ntatatat y fyty 4nt3y. исло anty 2400 22 Area of rancher A ny try zry To find prea dimension, optimized equation of area must be by ega x + 40 ya -4 3 put in egn 3 2 zzy an at (0) how 57 A 3 Naw tale derivative both side wornt a A! 2 +22 Floin the - sa 6) 8) 3 +8w 3 3 n-lew the 2 (20-100)

Now Fackr Cahical No. at n=30 also Al is positive Al is negative A 13 incoesny A B dersing. x 250 The sign chage of the derivatie from psitive to negative Indicares it is matimum Use first clasivative test to determine if so in may or mm 4 (50) + 3y = how 200 +3y ho 200 3 ya Was fect feet y 2 200 3. Dimension of vectiogle ranch anel * x 280 W0 3