Question

Y varies inversely as x : if y = 7 when x = 2/3, find y when x = 7

Answer 1

To find the new value of y when x equals 7 in an inverse variation problem, you first calculate the constant of variation with the given values, and then use this constant to solve for y given the new value of x.

Step-by-step explanation:

You're working with a concept in mathematics known as inverse variation, where y varies inversely as x. This can be mathematically expressed using the equation yx = k, where k is the constant of variation. To solve your problem, you first find the constant of variation when y = 7 and x = 2/3 by multiplying those values together. Once you have k, you can then find the new value of y when x = 7 by rearranging the equation to y = k/x and substituting the known values.

1. Find the constant k using the initial condition: k = yx = 7 * (2/3).
2. Calculate the value of k which is 14/3.
3. Use the constant k to find the new value of y when x = 7: y = k/7 = (14/3) / 7.
4. Simplify the expression to get the value of y.