help needed on more apps of calculus (1 Viewer)

[Petinga]

1. The perimeter of a circular sector is 20cm. The radius is increasingf 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 arta changing when the rdaius length is 10cm?

2. A ladder 5m long has its upper end against a vertical wall and its lower end on the horizonatl floor. The lower end moves way from the wall at a constant speed of 1m/s. Find the speed at which the upper end moves down the wall 4 seconds after the lower end has left the wall.

3. A vessel has such a shape that when the depth of the water in it is xcm, the voluime of water is vcm^3 where V=108x + x^3. water is pouired into the vessel at a constant rate of 30cm^3/second. At what rate is the level of water rising when the depth is 8cm?

 

[FinalFantasy]

I can guess that ur "rdaius" is radius...
but what is "arta"?

 

[FinalFantasy]

1. The perimeter of a circular sector is 20cm. The radius is increasingf 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 arta changing when the rdaius length is 10cm?

2. A ladder 5m long has its upper end against a vertical wall and its lower end on the horizonatl floor. The lower end moves way from the wall at a constant speed of 1m/s. Find the speed at which the upper end moves down the wall 4 seconds after the lower end has left the wall.

3. A vessel has such a shape that when the depth of the water in it is xcm, the voluime of water is vcm^3 where V=108x + x^3. water is pouired into the vessel at a constant rate of 30cm^3/second. At what rate is the level of water rising when the depth is 8cm?

2)let distance of lower end to wall be x
so dx\dt=1 m\s
let distance from upper end to the bottom be y
den use dy\dt=dy\dx * dx\dt
get y in terms of x den u can get dy\dx
3)V=x³+108x
dV\dx=3x²+108
dV\dt=30 cm³\s
rate of water lvl rising is
dx\dt=dx\dV * dV\dt

den put in da values

 

[FinalFantasy]

"1. The perimeter of a circular sector is 20cm. The radius is increasingf 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 arta changing when the rdaius length is 10cm?"

arc length=r@
so perimeter: r@+r+r=r@+2r=20
r(@+2)=20
r=20\(@+2)
dr\d@=...

dr\dt=5 cm\s (given)

so rate of angle of sector changing: d@\dt=d@\dr * dr\dt
juz put da stuffs in

area of sector, A=1\2 r²@
dA\dr=r@
rate the area is changing: dA\dt=dA\dr * dr\dt
den u put da things in