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
Answer:
(-8/7 ; 5/7)
Step-by-step explanation:
5t + 1/2s = 3 - - - (1)
3t - 6s = 9 - - - - - (2)
Multiply (1) by 12 and (2) by 1
Add the result to eliminate s
60t + 6s = 36
3t - 6s = 9
____________
63t = 45
t = 45 / 63
t = 5/7
Put t = 5/7 in either (1) or (2) to obtain the value of s
3(5/7) - 6s = 9
15/7 - 6s = 9
-6s = 9 - 15/7
-6s = (63 - 15)/7
-6s = 48/7
s = 48/7 * - 1/6
s = - 8/7
Answer:
I'd say A because this question is just like y and xays.
Step-by-step explanation:
Y = 18 x² + m x + 2
Exactly one x - intercept is for:
D = m² - 4 · 18 · 2 = 0
m² - 144 = 0
m² = 144
Answer:
m = -12 or m = 12
Answer:
John is running faster.
Step-by-step explanation:
Given that:
Average Speed of Anne = 6 miles per hour
Speed of John can be represented in the table below:
To find:
Who is running faster of the both i.e. Anne and John?
Solution:
Here, to find the faster runner we can compare the average speed of both the runners.
We are given that, average speed of Anne = 6 miles per hour
We will have to calculate the average speed of John to find the faster runner.
<em>Average speed</em> can be calculated by dividing the total distance traveled with the total time taken.
Total distance traveled by John = 11.5 - 1 = 10.5 miles
Total time taken by John = 1.5 hours
Average speed of John = 
Clearly Average speed of John is greater than that of Anne's.
Therefore, <em>John runs faster</em>.
