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प्रश्न
Observe the toothpick pattern given below:
(a) Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 4 | 13 |
(b) Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from 0 to 10 and the vertical axis from 0 to 30.
(c) Use your graph to predict the number of toothpicks in patterns 7 and 8. Check your answers by actually drawing them.
(d) Would it make sense to join the points on this graph? Explain.
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उत्तर
(a) On the basis of given patterns, we can arrange the following table which show the number of toothpicks in the first six terms.
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 4 | 7 | 10 | 13 | 16 | 19 |
Pattern and toothpicks shows the following relation as
1 → 4, 2 → 4 + 3 = 7
3 → 7 + 3 = 10, 4 → 10 + 3 = 13
5 → 13 + 3 = 16, 6 → 16 + 3 = 19
(b) On the basis of given condition, we can draw the following graph
(c) The graph follows the y = 3x + 1 pattern. If x = 7, then y = 3 × 7 + 1 = 21 + 1 = 22 and if x = 8, then y = 3 × 8 + 1 = 24 + 1 = 25.
| x | 7 | 8 |
| y | 22 | 25 |
(d) Yes, it shows the relation between x and y follows the given pattern y = 3x + 1.
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संबंधित प्रश्न
Plot the following points on a graph sheet. Verify if they lie on a line
A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
Locate the points:
(2, 1), (2, 2), (2, 3), (2, 4)
Find the coordinates of points A, B, C, D in Fig. 27.7.
In the given graph the letter that indicates the point (0, 3) is ______.
Match the coordinates given in Column A with the items mentioned in Column B.
| Column A | Column B |
| (1) (0, 5) | (a) y coordinate is 2 × x - coordinate + 1. |
| (2) (2, 3) | (b) Coordinates of origin. |
| (3) (4, 8) | (c) Only y–coordinate is zero. |
| (4) (3, 7) | (d) The distance from x-axis is 5. |
| (5) (0, 0) | (e) y coordinate is double of x-coordinate. |
| (6) (5, 0) | (f) The distance from y-axis is 2. |
Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order.
(1, 2), (2, 4), (3, 6), (4, 8)
If y-coordinate is 3 times x-coordinate, form a table for it and draw a graph.
Explain the situations represented by the following distance-time graph.
Ajita starts off from home at 07.00 hours with her father on a scooter that goes at a uniform speed of 30 km/h and drops her at her school after half an hour. She stays in the school till 13.30 hours and takes an auto-rickshaw to return home. The rickshaw has a uniform speed of 10 km/h. Draw the graph for the above situation and also determine the distance of Ajita’s school from her house.
