The Animal World Safari Park is a rectangular piece of land with an area of 323 square miles. The length of the park is 17 miles
2 answers:
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Answer:
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
and V(0) = 900
where A is a real constant, it appears because it says that the change i volume (dV/dt) is "proportional" to . 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.
Here again appears a constant B for the "proportional" part. And i wrote the velocity as "the rate of change of the position with respect to te time".
Suppose
At the same time, we can write
Note that (just reverse the sum). Let's pair the first terms of
and
, and the second, and the third, and so on:
Now, each grouped term in the sum on the right side adds to 151. There are 52 grouped terms on that same side (because there are 50 numbers in the range of integers 51-100, plus 50 and 101), which menas
But , as we pointed out, so