5. After 6 hours, the concentration is halved. After 12 hours, it will be quartered. If the original concentration is 200 nmol, a quarter is 50 nmol.
14. The population doubles after 3 hours, and a day is 24 hours. That means that the original population should be multiplied by , or
. 3 million times
is 3 * 256 million, or 768 million.
15. The concentration is halved every 8 hours and the original concentration is 100 nmol. So now, how many times do you halve 100 to get to 12.5?
100/2 = 50, 50/2 = 25, 25/2 = 12.5. That's three times. 3 * 8 is 24 hours, or 1 day.
Answer:
the volume of the sphere is
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, sphere and cube.
Given data
Volume of cube v = 64 cubic inches
since we are dealing with a cube the height and the radius of the sphere is same as the sides of the cube,
we know that volume of cube is expressed as
also diameter d=length l
Diameter d=
Radius r = =
=
Height h=
we know that the volume of a sphere is given by
substituting into the formula we have
9514 1404 393
Answer:
"complete the square" to put in vertex form
Step-by-step explanation:
It may be helpful to consider the square of a binomial:
(x +a)² = x² +2ax +a²
The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...
2a = 1
a = 1/2
That means we can write ...
(x +1/2)² = x² +x +1/4
But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:
_____
Another way to consider this is ...
x² +bx +c
= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*
= (x +b/2)² +(c -(b/2)²)
for b=1, c=1, this becomes ...
x² +x +1 = (x +1/2)² +(1 -(1/2)²)
= (x +1/2)² +3/4
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* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).