Matt is a short put champion and is planning to participate in the next Olympic Games. He starts to practice and completes 49 throws from a center point in different directions. When he started to measure all the distances,
he found that every throw landed in a spot 1-ft away from the previous one. In addition, the line connecting center point and the new spot always was perpendicular to the line connecting the new spot and the previous spot. If his last throw distance was 1 feet, how
much distance was his very first throw?
49
i think the answer is wrong
To find out the distance of Matt's very first throw, we need to analyze the given information.
We know that Matt completed 49 throws, and each throw landed 1 foot away from the previous one. So, we can infer that the distances form an arithmetic sequence with a common difference of 1 foot.
The formula for finding the nth term of an arithmetic sequence is given by:
nth term = a + (n - 1) * d
Where:
nth term represents the distance of the nth throw,
a represents the first term (distance of the first throw),
n represents the position of the term in the sequence,
d represents the common difference between the terms.
In this scenario, we are looking for the first throw, which corresponds to the first term of the sequence (a). So, we need to find the value of "a" in the formula.
From the given information, we know that the last throw distance was 1 foot. Using the formula, we can substitute the values into the equation:
1 = a + (49 - 1) * 1
Simplifying the equation:
1 = a + 48
Subtracting 48 from both sides of the equation:
a = 1 - 48
a = -47
Therefore, the distance of Matt's very first throw was -47 feet. However, it seems unlikely for a shot put competition, as distances are measured in positive values. It's possible that there might be a mistake in the given information or the question itself.