Calculus
posted by Nancy on .
In a right triangle, if one leg (adjacent to 90 degrees) is 10cm, which is increasing at the speed of 2cm/s; and another leg is 24 cm, which is decreasing at 2cm/s. how fast is the hypotenuse changing at this time?

c^2 = a^2+b^2
2c dc/dt = 2a da/dt + 2b db/dt
when a=10 b=24, c=26. Factoring out the 2 everywhere,
13 dc/dt = 10(2) + 24(2)
13 dc/dt = 28
dc/dt = 28/13