Question

Estimate the value of 6 x v2. Which of the following choices is the best estimate?

• 8.4
• 6.4
• 9.8
• 7.1

Answer 1

To estimate the value of \(6 \times v^2\), we need to make an assumption or have an estimate for \(v\).

Generally, if we don't have a specific value for \(v\), we can make a reasonable guess. However, since you mentioned "v2", we might assume it to be the square root of 2, which is around 1.414.

If we take \(v \approx 1.4\) (as a rounded estimate):

\[
v^2 = (1.4)^2 = 1.96 \approx 2
\]

Now, calculate \(6 \times v^2\):

\[
6 \times v^2 \approx 6 \times 2 = 12
\]

That value does not correspond to any of the options provided.

Instead, if we assume \(v\) to be closer to \(1\):

\[
v \approx 1 \Rightarrow v^2 = 1
\]

Then:

\[
6 \times v^2 = 6 \times 1 = 6
\]

Again, this value is not close to the choices given.

The choices might hint that \(v\) is around \(1.5\):

If \(v = 1.5\):

\[
v^2 = (1.5)^2 = 2.25
\]

Then:

\[
6 \times v^2 = 6 \times 2.25 = 13.5
\]

Let's explore \(v \approx 1.2\):

\[
v^2 = (1.2)^2 = 1.44
\]

Then:

\[
6 \times 1.44 = 8.64
\]

Looking at the estimates, the closest answer to \(8.64\) is \(8.4\).

Therefore, the best estimate for \(6 \times v^2\) based on reasonable assumptions for \(v\) is:

**8.4**