1)what is the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 8,9, and 10?

2) The square root of the difference of (B^2 /16) and (b^2/25)

3) Mr. Baker is 30 years old when his son is 4 years old. In how many years will Mr. Baker be five times as old as his son.
^I got 2 and 1/2

LCM(8,9,10) = 360

so, 361 will leave a remainder of 1 when divided by any of 8,9,10

(b^2/16)-(b^2/25) = 9b^2/400
so, the root is 3b/10

I agree with you on #3, but it's strange that the answer is not a whole number.

1) To find the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 8, 9, and 10, we can use the concept of the least common multiple (LCM).

The LCM of 8, 9, and 10 is the smallest multiple that is divisible by all three numbers. By determining the LCM of these numbers, we can find the answer to the question.

Start by finding the prime factorization of each number:
8 = 2^3
9 = 3^2
10 = 2 * 5

To find the LCM, take the highest power of each prime factor that appears. In this case, the highest power of 2 is 3, the highest power of 3 is 2, and the highest power of 5 is 1.

Multiply these highest powers together:
LCM = 2^3 * 3^2 * 5 = 360

Now, add 1 to the LCM:
360 + 1 = 361

Therefore, the smallest integer greater than 1 that leaves a remainder of 1 when divided by 8, 9, and 10 is 361.

2) The square root of the difference of (B^2 / 16) and (b^2 / 25) can be calculated step by step as follows:

First, simplify each fraction:
B^2 / 16 = (B/4)^2
b^2 / 25 = (b/5)^2

Now, subtract the simplified fractions:
(B/4)^2 - (b/5)^2

The difference of two squares can be factored using the identity a^2 - b^2 = (a + b)(a - b). In this case, let a = B/4 and b = b/5.

Therefore, the square root of the difference becomes:
√[(B/4 + b/5)(B/4 - b/5)]

Simplifying further, we have:
√[(5B + 4b)(5B - 4b)] / 20

So, the square root of the difference of (B^2 / 16) and (b^2 / 25) is √[(5B + 4b)(5B - 4b)] / 20.

3) To calculate in how many years Mr. Baker will be five times as old as his son, let's analyze the given information.

Currently, Mr. Baker is 30 years old, and his son is 4 years old. In x years, Mr. Baker's age will be 30 + x and his son's age will be 4 + x.

According to the problem, we need to find the value of x for which Mr. Baker's age will be five times his son's age. This can be represented as:

30 + x = 5(4 + x)

Now, solve the equation for x:

30 + x = 20 + 5x

Simplifying, we get:
4x = 10

Dividing both sides by 4, we find:
x = 10 / 4 = 2.5

Therefore, it will take 2.5 years for Mr. Baker to be five times as old as his son.