Chapter 6: Problem 2

Consider the parametric equations \(x=+\sqrt{t}, y=t\), for \(0 \leq t \leq 10\) (a) Draw up a table of values of \(t, x\) and \(y\) for values of \(t\) between 0 and 10 (b) Plot a graph of this function. (c) Obtain an explicit equation for \(y\) in terms of \(x\).

Short Answer

Expert verified

Question: Given the parametric equations \(x = \sqrt{t}\) and \(y = t\), find the explicit equation for y in terms of x. Answer: Using the process of substitution and elimination, we obtained the explicit equation for y in terms of x as \(y = x^2\).

Step by step solution

Create a table of values for t, x, and y

To create the table of values, we need to plug in the given range of t values into the parametric equations and find the corresponding x and y values: \(x = \sqrt{t}\) \(y = t\) We will do this for t values from 0 to 10.

Plot the graph of this function using the table of values

Using the table of values from Step 1, we can plot the points on a coordinate grid to get an idea of the function's graph. The points will be (x, y) coordinates for each corresponding value of t.

Obtain the explicit equation for y in terms of x

To find the explicit equation for y in terms of x, we need to eliminate t from the given parametric equations: 1. \(x = \sqrt{t}\) 2. \(y = t\) First, let's solve equation (1) for t: 1.' \(t = x^2\) Now, substitute the expression from equation 1.' into equation 2: 2.' \(y = x^2\) So the explicit equation for y in terms of x is given by: \(y = x^2\)

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Consider the parametric equations \(x=+\sqrt{t}, y=t\), for \(0 \leq t \leq 10\) (a) Draw up a table of values of \(t, x\) and \(y\) for values of \(t\) between 0 and 10 (b) Plot a graph of this function. (c) Obtain an explicit equation for \(y\) in terms of \(x\).

Short Answer

Step by step solution

Create a table of values for t, x, and y

Plot the graph of this function using the table of values

Obtain the explicit equation for y in terms of x

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