Find an expression for the nth term (tn) in each of the following sequence:
2 answers:
Answer:
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Work Shown:
The first term is a = 2 and the common difference is d = 4, since we're adding 4 to each term to get the next term.
Which is the answer.
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If you were to plug in say n = 3, then we get
showing that 10 is the third term, which matches with what the original sequence shows. I'll let you check the other values of n to fully confirm the answer.
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Answer:
The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.
Step-by-step explanation:
This is a problem of optimization.
We have to minimize the time it takes for the lifeguard to reach the child.
The time can be calculated by dividing the distance by the speed for each section.
The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.
Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:
Then, the time (speed divided by distance) is:
To optimize this function we have to derive and equal to zero:
As , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.
