There is a mountain with 45 bat caves in a row. Every cave has at least 2 bats and there are 490 bats in all. Any 7 caves in a row contain exactly 77 bats. Suppose the first cave has 7 times more bats than the last cave. What is the greatest possible number of bats in the 30th cave?

12 bats

Step-by-step explanation:

Let us number the bat caves from 1 to 45 and divide them into 5 parts:

a) 1

b) 2 to 29 ( bats)

c) 30

d) 31 to 44 ( bats)

e) 45

It is given that any 7 caves in a row has 77 bats. Hence, the total number of bats in part b and d = bats.

There remains bats in cave number 1, 30 and 45.

Now, our question demands the maximum possible number of bats in cave 30.

Minimum number of bats in a cave is 2. So we shall put 2 bats in the last cave, which gives us bats in the first cave.

Therefore, the number of bats in cave number 30 = bats.

5 pm

step-by-step explanation:

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.