Question

Substitute the given values into each given formula and solve for the unknown variable. T = 9, d = 63

P = 32, W = 7
V = 40, h = 8
I = 23, p = 230, r = 0.02

Answer 1

1.
`\(T = (d)/(s)\)`: The unknown variable
`\(s\) is \(7\)`.

2.
`\(P = (W)/(t)\)`: The unknown variable
`\(t\) is \((7)/(32)\).`

3.
`\(V = (1)/(3) \pi r^2 h\)`: The unknown variable
`\(r\) is \(\sqrt{(40 * 3)/(8 * \pi)}\)`.

4.
`\(I = prt\)`: The unknown variable
`\(t\) is \((23)/(230 * 0.02)\)`.

Let's substitute the given values into each formula and solve for the unknown variable.

1. Formula:
`\(T = (d)/(s)\)`

- Given values:
`\(T = 9\), \(d = 63\)`

- Substitute and solve:
`\(9 = (63)/(s)\)`

- Solve for
`\(s\): \(s = (63)/(9) = 7\)`

So, the unknown variable
`\(s\) is \(7\)`.

2. Formula:
`\(P = (W)/(t)\)`

- Given values:
`\(P = 32\), \(W = 7\)`

- Substitute and solve:
`\(32 = (7)/(t)\)`

- Solve for
`\(t\): \(t = (7)/(32)\)`

So, the unknown variable
`\(t\) is \((7)/(32)\)`.

3. Formula:
`\(V = (1)/(3) \pi r^2 h\)`

- Given values:
`\(V = 40\), \(h = 8\)`

- Substitute and solve:
`\(40 = (1)/(3) \pi r^2 * 8\)`

- Solve for
`\(r^2\): \(r^2 = (40 * 3)/(8 * \pi)\)`

- Solve for
`\(r\): \(r = \sqrt{(40 * 3)/(8 * \pi)}\)`

So, the unknown variable
`\(r\) is \(\sqrt{(40 * 3)/(8 * \pi)}\)`.

4. Formula:
`\(I = prt\)`

- Given values:
`\(I = 23\), \(p = 230\), \(r = 0.02\)`

- Substitute and solve:
`\(23 = 230 * 0.02 * t\)`

- Solve for
`\(t\): \(t = (23)/(230 * 0.02)\)`

So, the unknown variable
`\(t\) is \((23)/(230 * 0.02)\)`.