Rates of Change: Sector and Kite (1 Viewer)

[.ben]

4. The perimeter of a circular sector is 20cm. The radius is increasing at the rate of 5cm/s. At what rate is the angle of the sector changing when the radius length is 10cm? Also at what rate is the area changing when the radius length is 10cm?

11. A kite, 50 metres high, is being carried horizontally by the wind at a rate of 4m/sec. How fast is the string being let out, when the length of the string is 100 metres?

Thanks

 

[pLuvia]

4)
You need to find dθ/dt=dθ/dr*dr/dt
Which you already know dr/dt=5
Using l=rθ, find dθ/dr. Then sub in r=10 and you should get dθ/dt

11)
Let l be the length of the string
You need to find dl/dt=dl/dx*dx/dt
Which you know dx/dt=4
Draw a triangle with height 50, length x and hypotenuse l, and find an expression for l in terms of x then you can find dl/dx. Sub in the value for 100 and you should get your answer

 

[.ben]

Ok thanks pluvia