Question

3. В соревновании по стрельбе за каждый промах в серии из 25 выстрелов стрелок получал штрафные очки: за первый промах — одно штрафное очко, за каждый последующий — на 0,5 очка больше, чем за предыдущий. Сколько раз попал в цель стрелок, получивший 7 штрафных очков?

Answer 1

1 промах- 1 , 2 промах-1,5, 3 промах- 2, 4 промах- 2,5
1+1,5+2+2,5=7
25-7=21 раз попал в цель

Answer 2

Calculation of Shots and Penalty Points

To determine the number of shots the shooter hit the target, we need to calculate the number of penalty points received.

According to the given information, for each miss in a series of 25 shots, the shooter receives penalty points. The first miss results in one penalty point, and each subsequent miss incurs an additional 0.5 penalty points more than the previous one.

Let's calculate the number of penalty points received by the shooter, which will help us determine the number of shots that hit the target.

1. The shooter received a total of 7 penalty points.

To find the number of shots that hit the target, we can work backward from the penalty points. Starting with the highest penalty points, we subtract the penalty points for each miss until we reach zero.

Let's calculate the number of shots that hit the target:

- The shooter received 7 penalty points. - The first miss incurs one penalty point. - The second miss incurs 0.5 penalty points more than the first miss. - The third miss incurs 0.5 penalty points more than the second miss. - And so on.

We can set up an equation to solve for the number of shots that hit the target:

1 + (1 + 0.5) + (1 + 0.5 + 0.5) + ... + (1 + 0.5 + 0.5 + ...)

Let's simplify the equation:

1 + 1.5 + 2 + 2.5 + ...

This is an arithmetic series with a common difference of 0.5 and an unknown number of terms.

To find the number of terms, we can use the formula for the sum of an arithmetic series:

Sn = (n/2)(2a + (n-1)d)

Where: - Sn is the sum of the series - n is the number of terms - a is the first term - d is the common difference

In our case: - Sn = 7 (the total penalty points) - a = 1 (the first term) - d = 0.5 (the common difference)

Let's solve for n:

7 = (n/2)(2*1 + (n-1)*0.5)

Simplifying the equation:

7 = (n/2)(2 + 0.5n - 0.5)

7 = (n/2)(1.5n + 1.5)

Multiplying both sides by 2:

14 = n(1.5n + 1.5)

Expanding the equation:

14 = 1.5n^2 + 1.5n

Rearranging the equation:

1.5n^2 + 1.5n - 14 = 0

We can solve this quadratic equation to find the value of n.

Using the quadratic formula:

n = (-b ± √(b^2 - 4ac)) / (2a)

Where: - a = 1.5 - b = 1.5 - c = -14

Let's calculate the value of n using the quadratic formula:

n = (-1.5 ± √(1.5^2 - 4*1.5*(-14))) / (2*1.5)

Simplifying the equation:

n = (-1.5 ± √(2.25 + 84)) / 3

n = (-1.5 ± √86.25) / 3

Taking the positive root:

n = (-1.5 + √86.25) / 3

n ≈ 4.19

Since the number of shots must be a whole number, we round down to the nearest whole number:

n ≈ 4

Therefore, the shooter hit the target 4 times, receiving a total of 7 penalty points.

Answer: The shooter hit the target 4 times, receiving 7 penalty points.