Help on Apps of calculus (1 Viewer)

[Petinga]

1. A particle moves on the circumference of the semicircle y= Sqare root 4 - x^2. Find dy/dt when x=1, if dx/dt = 4.


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

3. Rain is falling and is collected in an inverted cone so that the volume collected increases at a constant rate of 4 pie cm^3/hour. If the radius (r) of the cone is half its height (h), find the rate, in cm/hour, at which the height is increasing when h=3.

 

[haboozin]

1. A particle moves on the circumference of the semicircle y= Sqare root 4 - x^2. Find dy/dt when x=1, if dx/dt = 4.


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

3. Rain is falling and is collected in an inverted cone so that the volume collected increases at a constant rate of 4 pie cm^3/hour. If the radius (r) of the cone is half its height (h), find the rate, in cm/hour, at which the height is increasing when h=3.

question 1:

dy/dt = dx/dt . dy/dx

just diffrentiate y wrt x and plug in x = 1 and times it by 4.


Q2: right angle triangle

    x
---------
| <-50/
|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;/
|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;/
|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;/
|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;/ Srt (x^2 + 50^2)
|&nbsp;&nbsp;&nbsp;&nbsp;/
|&nbsp;&nbsp;&nbsp;/
|&nbsp;&nbsp;/
|&nbsp;/
|/
from data dx/dt = 4ms^-1

dl/dt = dx/dt . dl/dx

now diffrentiate Srt (x^2 + 50^2) and times by 4 again



Q3:


dv/dt = 4pi cm^3h^-1
r = 1/2h

you need dh/dt and to get that you must do the following
dh/dt = dv/dt * dh/dv

find the volume of a cone (i forgot what it is) substitute r with 1/2h
diffrentiate and inverse your diffrentiation eg 2 becomes 1/2.
this is because you found dv/dh but you need dh/dv. they are recipricals.
then you just times it by 4pi.

 

[Gova1802]

3 is 16/9 without pi

 

[Drongoski]

Gova - are you an archaeologist??