Answer:
Step-by-step explanation:
Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.
So, dV/dt = 0.03.
We want to show that dS/dt is directly proportional to 1/r.
In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.
First, the volume of a sphere V is given by:
Therefore:
Next, the surface area of a sphere S is given by:
Therefore:
We can divide both sides by 2:
We can substitute this into dV/dt. Rewriting:
So:
Since dV/dt = 0.03 or 3/100:
Therefore:
Where k = 3/50.
And we have shown that dS/dt is directly proportional to 1/r.
Answer:
The overall change is 116points gained
Step-by-step explanation:
Points gained = 12points
Points lost = 114points
Points gained = 218points
Unknown:
Overall change in its value = ?
Solution:
The overall change = Total points gained - Total points lost
= (218 + 12) - 114
= 116points
The overall change is 116points gained
Answer: $20
Step-by-step explanation:
8 divided by 12 = .67
.67 times 30
Answer:
"Let the smaller value a = <u>10</u> and the larger value b = <u>100</u>. Than a^2 + 2ab + b^2 is <u>10^2 + 2 * 10 * 100 + 100^2</u>. This can be simplified to <u>12100</u>. So, 110^2 is equal to <u>12100</u>."
Hope this helped!
Answer:
$16,640
Step-by-step explanation:
Tim's total annual wage expense is ...
($8.00 /h)(40 h/wk)(52 wk/yr) = $8×40×52 /yr = $16,640 per year