Math Problem Statement

Table 1 shows the values of two variables, x and y, obtained from an experiment. A straight line will be obtained when a graph of 1/y against x^2 is plotted. Based on the table, construct a table for x^2 and 1/y, plot the graph using the given scale, and answer the related questions about y and its expression in terms of x.

Solution

The question contains a table and instructions for mathematical tasks such as constructing a table, plotting a graph, and interpreting the results. Here's how we can approach each part based on the visible text in the image:


Instructions Breakdown:

  1. Part (a): Construct a table for x2x^2 and 1y\frac{1}{y}.

    • Use the given data for xx and yy from the table.
    • Compute x2x^2 for each value of xx.
    • Compute 1y\frac{1}{y} for each value of yy.
  2. Part (b): Plot 1y\frac{1}{y} against x2x^2.

    • Use a scale of 2 cm for x2x^2 (horizontal axis) and 0.5 unit for 1y\frac{1}{y} (vertical axis).
    • Draw the best-fit line through the points.
  3. Part (c): Use the graph from part (b) to answer:

    • (i)(i) Find the value of yy when x=1.6x = 1.6.
    • (ii)(ii) Express yy in terms of xx using the graph.

Would you like me to:

  1. Construct the table for x2x^2 and 1y\frac{1}{y}?
  2. Provide guidance on plotting the graph?
  3. Assist with the interpretation of the graph for part (c)?

Let me know how you'd like to proceed!

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Math Problem Analysis

Mathematical Concepts

Graph Plotting
Algebra
Functions
Linear Relationships

Formulas

x^2 = x * x
1/y = Reciprocal of y

Theorems

Linear relationship between variables when plotted against specific transformations

Suitable Grade Level

Grades 10-11