Answer:
43.83cm
Step-by-step explanation:
There are only two faces that are 25cm by 36cm, the top and the bottom face. Since, the ant, cannot move across the bottom face, we are left with the top face which is a rectangle. The shortest distance is through the diagonal.
Drawing a diagonal, you have two right-angled triangles. Bringing any out, we would need to know the length of the diagonal which is the hypotenuse of the right angle triangle. Using Pythagoras theorem:
(Hypotenuse)^2 = (opposite)^2 + (adjacent)^2
H^2 = 25^2 + 36^2
H^2 = 625 + 1296
H^2 = 1921
H = sqrt (1921)
H = 43.83 cm (to 2 d.p.)
H which represents the hypotenuse, that is the diagonal is the shortest distance. Hence, the shortest distance is 43.83cm.
3: Millions' place
4: Hundred thousand's place
2: Ten thousands' place
9: Thousands' place
1: Hundreds' place
1: Tens' place
1: One's place
Thus your answer is: Hundred thousands' place
It's less than because 5 is greater than -2x - 1
A good place to start is to set to y. That would mean we are looking for to be an integer. Clearly, , because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since is a radical, it only outputs values from , which means y is on the closed interval: .
With that, we don't really have to consider y anymore, since we know the interval that is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:
Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.