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".
The answers to the blanks are
1. 600,
2. 120,
3. 120,
4. 180.
Explanation:
- The fence means perimeter around the court. So a tennis court's perimeter is 600 feet fence. The perimeter of a rectangle is 2 times the sum of the rectangle's length and the rectangle's width.
- It is given that length equals 60 more than width i.e. l = w + 60, where l is the length of the court and w is the width of the court.
- The perimeter of a court = 600 = 2 (l + w) = 2l + 2w = 2 (w +60) + 2w, this becomes, 2w + 120 + 2w = 600; 4w = 480, w = 120.
- Since l = w + 60, l = 120 + 60 = 180. So length of a court is 180 feet and the width of a court is 120 feet.
If a person is not healthy, then he or she will find it very difficult to enjoy life. Balanced food, fresh air, exercise, good posture, plenty of rest, pure water, cleanliness, regular check-ups at the doctor and dentist " all helps keep our body machines running as they should.
A fit person is also more resistant to illnesses. The simplest way of keeping fit is by exercising regularly. But the exercises must be vigorous. Secondly we have to watch what we are eating. There should be enough fibre, protein, fruit, vegetables and vitamins. And of course our bodies need water. Water allows our blood to flow through the blood vessels thus supplying the body with vital nutrients. We must drink about six glasses a day.
We have to get enough sleep. All of us know how cranky we can get if we do not have enough sleep. And what's more " avoid stress, worry and tension, think positive! A bath or a shower every day is a good habit. It makes us clean but it also helps us to fall asleep better. Brushing our teeth is part of keeping clean.
48 inches cubed is the answer
The first step to solve this problem is to find the area of
the rectangular piece of fabric.
A of triangle = bh/2
A = (14 cm) (6 cm) /2
A = 84 cm^2 / 2
A = 42 cm
And since there are 31 pieces of the fabric, the total area
of all the pieces of fabric is:
31 pieces of fabric x 42 square centimeters per piece =
1,302 square centimeters
To computer how many congruent triangular patches can be
cut, you have to divide the total area of the fabric pieces with the area of
the congruent triangle:
1,302 square centimeters / 21 square centimeters = 62
Therefore, Leia can cut 62 patches.
