Answer:
28.27 cm/s
Step-by-step explanation:
Though Process:
- The punch glass (call it bowl to have a shape in mind) is in the shape of a hemisphere
- the radius
- Punch is being poured into the bowl
- The height at which the punch is increasing in the bowl is

- the exposed area is a circle, (since the bowl is a hemisphere)
- the radius of this circle can be written as

- what is being asked is the rate of change of the exposed area when the height
- the rate of change of exposed area can be written as
. - since the exposed area is changing with respect to the height of punch. We can use the chain rule:

- and since
the chain rule above can simplified to
-- we can call this Eq(1)
Solution:
the area of the exposed circle is

the rate of change of this area can be, (using chain rule)
we can call this Eq(2)
what we are really concerned about is how
changes as the punch is being poured into the bowl i.e 
So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

and rearrage the formula so that a is the subject:

now we can derivate a with respect to h to get 

simplify

we can put this in Eq(1) in place of 
and since we know 

and now we use substitute this
. in Eq(2)

simplify,

This is the rate of change of area, this is being asked in the quesiton!
Finally, we can put our known values:

from the question


The answer is B since he bought 4 in all it is x+y =4 . x=dvd y= blue ray discs .
so 2x + 5y =11
2x since dvds are $2
5y since blue ray discs are $5
11 since that’s the total
Answer:
20 ft
Step-by-step explanation:
Answer:
200 Meters per minute
Step-by-step explanation:
Amanda went 180mpm constantly for 15 minutes. 180 times 15= 2700.
5700-2700=3000
3000 meters divided by 15 minutes= 200 meters per minute
Answer: 40
Step-by-step explanation: 600 divided by 15