The surface area of the sphere is:
A = 4 * pi * r ^ 2
Deriving we have:
A '= 8 * pi * r * r'
We clear the speed:
r '= A' / (8 * pi * r)
Substituting values:
r '= 24 / (8 * pi * 3)
r '= 1 / pi inch / sec
Then, the volume of the sphere is:
V = (4/3) * (pi) * (r ^ 3)
Deriving we have:
V '= (3) * (4/3) * (pi) * (r ^ 2) * (r')
Substituting values:
V '= (3) * (4/3) * (pi) * (3 ^ 2) * (1 / pi)
Rewriting:
V '= (4) * (9)
V '= 36 inch3 / sec
Answer:
the volume of the ice is changing at 36 inch3 / sec at that moment
The fence is 210 ft long.
There is a post every 3.5 ft.
If you divide 210 ft by 3.5 ft, you get the number of spaces between posts.
(210 ft)/(3.5 ft) = 60
The fence starts with a post. Then there is 3.5 ft of fencing. Then there is another post. Then there is another 3.5 ft of fencing followed by a post. In total there are 61 posts.
Here's another way of thinking of why you end up with 60 posts.
For each 3.5 ft of fencing, you place a post at the end of the fencing.
Since there are 60 3.5-ft-long pieces of fencing, there will be 60 posts, one at the end of each piece of fencing. The first thing that is done is to put the initial post before any fencing is put up. The first post plus 60 more posts add up to 61 posts.
Now that you see why there are 61 posts, we can calculate their cost.
61 * $8.50 = $518.50
Answer:
Equation: x + (x+ 1) = 67
Step-by-step explanation:
We want to find two consecutive integers.
Let them be labeled as x and x + 1
We want x + (x + 1) = 67
x is the smaller number
x + 1 is the largest
We can solve for x.
x + (x + 1) = 2x + 1 = 67
2x = 66
x = 33
The largest integer is 34
Answer:
A for first one and C
Step-by-step explanation:
Answer:
$675.00
Step-by-step explanation:
4500 x 0.05 x 3 = 675
