Numbers can be expressed, ordered and compared by a lot of
mathematical principles, properties, models and paradigms. There are different
properties of numbers to associate, group and distribute numbers. For example
commutative property of addition, 1 + 2 = 3 can be 3 = 1 + 2. Moreover, numbers
can be expressed by mathematical form, thus 100 wherein 1 is in the place order
of hundreds. And so on… other examples can be mathematical symbols or
inequality to compare numbers. For example, 1 > 2. One is less than 2.
Answer:
Step-by-step explanation:
The answer is factor the trinomial
If these triangles are congruent, then side RS is congruent to side TV and that means that y = 4 - x. If y = 4-x, we can sub that into the next equation where side RV = side ST and 1 = 4x - y. If y = 4-x, we sub in accordingly to get 1 =4x - (4 - x). That simplifies to 1 = 4x - 4 + x which is, combining like terms, 5 = 5x. That means that x = 1. If x = 1, and y = 4 - x, then y = 4 - 1 and y = 3. There you go!
2s+5<span>≥49
First: Subtract 5 on both sides
You'll get: 2s </span><span>≥ 44
Last: Divide each side by 2 so your s would be alone
You'll get: s </span><span>≥ 22 <That would be your answer
HOPE THIS HELPS! ^_^</span>
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
