# Calculus

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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?

• Calculus -

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

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