a) he rate of change of the volume of a snowball (due to melting) is proportional to the square of the volume at time t. Initially, the snowball has a volume of 900 cm3

$\frac{dV(t)}{dT} = A*V(t)^{2} \\$ and V(0) = 900 $cm^{3}$

where A is a real constant, it appears because it says that the change i volume (dV/dt) is "proportional" to $V(t)^{2}$ . Furthermore, we should assume that A is a negative number, because the volume of the snowball will decrease as the time pasese by.

(b) For an insect moving along some path, the velocity at time t is proportional to the square root of its position.

$\frac{dr(t)}{dt} = B*\sqrt{r(t)}$

Here again appears a constant B for the "proportional" part. And i wrote the velocity as $\frac{dr(t)}{dt}$ "the rate of change of the position with respect to te time".

7 0

3 years ago

What is the common ratio for the geometric sequence? 32, 8, 2, 12, ... Enter your answer in the box.

mamaluj [8]

Answer:

Given sequence is not a geometric progression and there will be no common ration for this sequence.

Step-by-step explanation:

Need to determine common ration for the following geometric sequence

32, 8, 2, 12, ...

In given geometric sequence

a1 = 32, a2=8, a3=2, a4=12 ……….

Common ratio = $\frac{a_2}{a_1} =\frac{a_3}{a_2} =\frac{a_4}{a_3}$

$\frac{a_2}{a_1}=\frac{8}{32}=\frac{1}{4}$

$\frac{a_3}{a_2} =\frac{2}{8}=\frac{1}{4}$

$\frac{a_4}{a_3}=\frac{12}{2}=6$

Since $\frac{a_2}{a_1}=\frac{a_3}{a_2}\neq\frac{a_4}{a_3}$ so we can say that given sequence is not a geometric progression and there will no no common ration for this sequence.