Math 220 March 7 I. If 1200 cm2 of material is available to make a ...
Math 220 March 7 I. If 1200 cm2 of material is available to make a ...
Math 220 March 7 I. If 1200 cm2 of material is available to make a ...
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T (x) = 1<br />
5<br />
T ′ (x) = 1<br />
5 +<br />
1<br />
(x) + 1502 + (200 − x) 2<br />
2<br />
−400 + 2x<br />
4 1502 + (200 − x) 2<br />
0 = 1<br />
5 +<br />
−400 + 2x<br />
4 1502 + (200 − x) 2<br />
1<br />
5 =<br />
400 − 2x<br />
4 1502 + (200 − x) 2<br />
( 1<br />
5 )2 400 − 2x<br />
= (<br />
4 1502 )2<br />
+ (200 − x) 2<br />
1<br />
25 =<br />
4(200 − x) 2<br />
16(1502 + (200 − x) 2 )<br />
1<br />
25 =<br />
(200 − x) 2<br />
4(1502 + (200 − x) 2 )<br />
4(150 2 + (200 − x) 2 ) = 25(200 − x) 2<br />
300 2 + 4(200 − x) 2 = 25(200 − x) 2<br />
21(200 − x) 2 = 300 2<br />
(200 − x) 2 = 30000<br />
<br />
7<br />
30000<br />
200 − x = ±<br />
7<br />
<br />
30000<br />
x = 200 ±<br />
7<br />
x = 134.535, 265.465<br />
<br />
30000<br />
T (x) < 0 when x < 200 −<br />
7<br />
<br />
30000<br />
T (x) > 0 when x > 200 −<br />
7<br />
There <strong>is</strong> a minimum at x = 134.535<br />
The dog should run 134.535 feet before jumping in the water.<br />
7
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