5.5.4
1
If y varies inversely with the square of x, and y = 13 when x = 2, find y when x = 0.5.

y = 208

Step-by-step explanation:

We need to solve this problem, we need to interpret the question

y varies inversely means 1/

y varies inversely with the square of x

That's y varies /x^2

To equate it, we need to add a constant K

y = K * 1/x^2

y = K/x^2

As we've been provided with some information

y = 13

x = 2

Inserting into

y = K/x^2

13 = K/2^2

13 = K/4

K = 13 * 4

K = 52

Our constant is 52

Provided on the another information we are given to find y, x = 0.25

Using the same formula

y = K/x^2

K = 52

x = 0.25

y = 52/0.25

y = 208

The new value of y is 208 when x = 0.25

  about 5.6 days

step-by-step explanation:

we can fill the given information into the decay equation and solve for the value of t at which half the sample remains.

the half-life is about 5.6 days.