Question

1.At noon of a certain day,ship A is ^0 km due north of ship B. If A sails east at 12 km/hr and B sails north 9 km/hr,determine how rapidly the distance between them is changing 2 hrs later. Is it increasing or decreasing?

2.At a given instant the legs of a right triangle are 16 cm and 12 cm, respectively. The first leg decreases at 1/2 cm/min and the second increases at 2 cm/min. At what rate is the area increasing after 2 min?

Answer 1

#1 contains a typo,
fix the ^0

#2
let the first leg be x cm
and the second leg be y cm

given:
dx/dt = -.5
dy/dt = 2
find: dA/dt , when t = 2

A = (1/2)xy
dA/dt = (1/2)(x dy/dt + y dx/dt)

at the given time of 2 minutes
x = 16 - 2(.5) = 15
y = 12 + 2(2) = 16

dA/dt = (1/2)(15(2) + 16(-.5) )
= 11

The area at that instant is increasing at 11 cm^2/min

check my arithmetic, I am only on my first coffee.

Answer 2

At noon of a certain day,ship A is 60 km due north of ship B. If A sails east at 12 km/hr and B sails north 9 km/hr,determine how rapidly the distance between them is changing 2 hrs later. Is it increasing or decreasing?