Answer:
This is absolute value equation so collect like terms and find X
15+5=|x|
20=|x|
since it's absolute value it's going to be 20 or -20
Answer:
$6
Step-by-step explanation:
let x and y be the number of chip and pretzel bags respectively :
4x%2B2y%3 C=20
:
if x=1 then 4%281%29%2B2y%3C=20--->{{2y<=16}}}--->y%3C=8 :
if x=3 then 4%283%29%2B2y%3C=20--->{{2y<=8}}}--->y%3C=4 :
so chips 1 and pretzels 8 :
chips 3 and pretzels 4.
To find the mid point add both X coordinates together and divide by 2 and then do the same with the y coordinates.
X coordinate: 4 + -6 = 4-6 = -2 / 2 = -1
Y coordinate: -2 + 3 = 1 / 2 = 1/2
Midpoint: ( -1, 1/2)
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


20% because there are 10 numbers and 2 of them are a multiple of 5. :)