Respuesta :
Answer:
(a) 31.75 mph
(b) 31.77 mph
Explanation:
(a) For t = 10 min = 10 / 60 = 1 / 6 hour
According to the question,
dx /dt = 15 mph
dy / dt = 28 mph
After 10 minutes
x = 1/6 x 15 = 2.5 miles
y = 1/6 x 28 = 4.67 miles
[tex]d = \sqrt{x^{2}+y^{2}}=\sqrt{2.5^{2}+4.67^{2}} = 5.3 miles[/tex]
According to diagram
[tex]D^{2} = {x^{2}+y^{2}}[/tex]
Differentiate both sides with respect to t.
2D dD/dt = 2 x dx/dt + 2y dy/dt
D dD/dt = x dx/dt + y dy/dt
5.3 dD/dt = 2.5 (15) + 4.67 (28)
dD/dt = 31.75 miles/hour
(b) For t = 55 minutes = 55 / 60 hours
After 55 / 60 hours
x = 55 / 60 (15) = 13.75 miles
y = 55 / 60 (28) = 25.67 miles
[tex]d = \sqrt{x^{2}+y^{2}}=\sqrt{13.75^{2}+25.67^{2}} = 29.12 miles[/tex]
According to diagram
[tex]D^{2} = {x^{2}+y^{2}}[/tex]
Differentiate both sides with respect to t.
2D dD/dt = 2 x dx/dt + 2y dy/dt
D dD/dt = x dx/dt + y dy/dt
29.12 dD/dt = 13.75 (15) + 25.67 (28)
dD/dt = 31.77 miles/hour
