Use the proportion 8/64 = 12/y. Cross multiply to get 8y = 768. Divide both sides by 8 to get y=96
Looking at this problem in terms of geometry makes it easier than trying to think of it algebraically.
If you want the largest possible x+y, it's equivalent to finding a rectangle with width x and length y that has the largest perimeter.
If you want the smallest possible x+y, it's equivalent to finding the rectangle with the smallest perimeter.
However, the area x*y must be constant and = 100.
We know that a square has the smallest perimeter to area ratio. This means that the smallest perimeter rectangle with area 100 is a square with side length 10. For this square, x+y = 20.
We also know that the further the rectangle stretches, the larger its perimeter to area ratio becomes. This means that a rectangle with side lengths 100 and 1 with an area of 100 has the largest perimeter. For this rectangle, x+y = 101.
So, the difference between the max and min values of x+y = 101 - 20 = 81.
Answer:
<em>The south celestial pole is the point in the sky directly above Earth's southern axis. It's the point around which the entire southern sky appears to turn. The height of the south celestial pole in your sky depends on your latitude.</em>
Step-by-step explanation:
Answer:
The solution set is the empty set.
Step-by-step explanation:
{x | x < 2} is the set of all numbers less than 2. This means x can take values such as 1.99, 0, -2000 and so on. That is, all values less than 2.
{x | x ≥ 2} is the set of all numbers equal to or greater than 2. This means x can take values such as 2, 2.1, 5000, and so on. That is, 2 or any value greater than 2.
Since there is no sign between the two sets, the question is asking for the intersection between these two sets. That is, what elements are common to these two sets? As we can see, the two sets don't have any common element. Hence, their intersection is the empty set.
(Note that the union of these two sets would be the set of all real numbers as that includes all elements from either set).
