A) The side length is 5 units since 5*5*5 = 125. You can guess and check to see which value multiplies with itself three times to get 125. Or you can take the cube root of 125 to get 5. You can type in 125^(1/3) to indicate you want the cube root of 125
b) The volume is 64 cubic units. Multiply the side length 4 by itself three times: 4*4*4 = 64.
Answer:
It takes 7.37 hours for the size of the sample to double.
Step-by-step explanation:
Continuous exponential growth model:
The continuous exponential growth model for populations is given by:

In which P(0) is the initial population and r is the growth rate parameter, as a decimal.
Growth rate parameter of 9.4% per hour.
This means that 
So


How many hours does it take for the size of the sample to double?
This is t for which P(t) = 2P(0). So







It takes 7.37 hours for the size of the sample to double.
Answer:
_______________________________________________The simplied version is:
_______________________________________________ "
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or; write as: "
" .
_______________________________________________Explanation:
_______________________________________________
Given:
_______________________________________________
"

" ;
_______________________________________________ → Factor out a "6v"

in the "numerator"; & factor out a "2" in the denominator; as follows:
____________________________________→

;
____________________________________→ "

" ;
______________________________________________or; factor out the "denominator" :
______________________________________________→ (v² + 13v + 42) = (v+7)(v+6) ;
______________________________________________and write as:
______________________________________________→ "
" .
______________________________________________
Step-by-step explanation:
Let's say R is the initial radius of the sphere, and r is the radius at time t.
The volume of the sphere at time t is:
V = 4/3 π r³
Taking derivative with respect to radius:
dV/dr = 4π r²
This is a maximum when r is a maximum, which is when r = R.
(dV/dr)max = 4π R²
This is 4 times the sphere's initial great circle area, but not the great circle circumference. The problem statement contains an error.