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Submarine word problem

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The movement of two submarines are being followed by a tracking system, and the positions of the submarines are modelled by points. The position of Sub A at time t is (2t+2, 2t+1) and the position of Sub B at time t is (4-t, t+5)
(distance in Kilometers)

1.How would I go about eliminating t from each pair of coordinates, and from this realise each Sub travels in a straight line?

2. How would I go about finding the distance between the Subs at each of the times t=0 and t=2?

3. If d is the distance between the pods at time t, how would I go about finding an expression for d squared in terms of t? And how would I go about completing the square for this expression, and show that the minimum value of d squared is attained when t =1?

4. And how would I go about finding the shortest distance between the Subs?

Solution Summary

This shows how to work with the movement of two submarines modelled by points based on an equation.

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Time And Distances
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The movement of two submarines are being followed by a tracking system, and the positions of the submarines are modelled by points. The position of Sub A at time t is (2t+2, 2t+1) and the position of Sub B at time t is (4-t, t+5)
(distance in Kilometers)

1.How would I go about eliminating t from each pair of coordinates, and from this realise each Sub travels in a straight line?

For the Sub A, its position at time t is (2t+2, 2t+1) which tells us
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Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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