A rocketship, travelling away from earth with a speed of 0.8c, sends regular radio signals which are received on Earth every 45.2 min. According to the rocketship astronauts, how frequently are the signals being sent?

I really need help. Its a basic question yet har for me.

Question: Find the only integer between 1500 and 2500 which is an integral multiple of both 2 to the power of 5 and 2 to the power of 5 subtract 1.

Christine can you please answer my question. Its a very kissy question since I am a kid. Search my post please.

To answer your first question:

When an object is moving at a high speed relative to an observer, time dilation occurs. This means that time appears to move slower for the moving object compared to the observer at rest. The formula for time dilation is:

t' = t / (sqrt(1 - v^2/c^2))

Where t' is the time experienced by the moving object, t is the time observed by the observer at rest, v is the relative velocity between the two objects, and c is the speed of light.

In this case, the rocketship is traveling at a velocity of 0.8c (80% of the speed of light). The time observed on Earth is 45.2 minutes.

Plugging in the values into the time dilation formula, we have:

t' = 45.2 / (sqrt(1 - 0.8^2))

Calculating this, we find that the time experienced by the astronauts on the rocketship is approximately 85.31 minutes.

Therefore, according to the rocketship astronauts, the signals are being sent approximately every 85.31 minutes.

Now, moving on to your second question:

We are looking for an integer between 1500 and 2500 that is a multiple of both 2^5 (32) and 2^5 - 1 (31).

To find this integer, we can start by finding the least common multiple (LCM) of 32 and 31. The LCM is the smallest number that is divisible by both numbers.

To find the LCM, we can list the multiples of each number and find the first common multiple:

Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320...

Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310...

We can see that the first common multiple is 992, which is greater than 1500. However, we need to find the closest common multiple that is less than 2500.

Next, we can list the multiples of 992 until we find one that is less than 2500:

Multiples of 992: 992, 1984, 2976, 3968, 4960...

We see that 1984 is the closest common multiple between 32 and 31 that is less than 2500 and greater than 1500. Therefore, the answer to your question is 1984.

I hope this helps!