To find the height of the rock after 3 seconds, we can use the given formula for height, which is [tex]\( H = 90 - 4.9x^2 \)[/tex].
We need to plug in [tex]\( x = 3 \)[/tex] seconds into the formula and solve for [tex]\( H \)[/tex].
1. Start with the formula:
[tex]\[
H = 90 - 4.9x^2
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the formula:
[tex]\[
H = 90 - 4.9(3)^2
\][/tex]
3. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
4. Substitute [tex]\( 9 \)[/tex] back into the formula:
[tex]\[
H = 90 - 4.9 \cdot 9
\][/tex]
5. Multiply [tex]\( 4.9 \)[/tex] by [tex]\( 9 \)[/tex]:
[tex]\[
4.9 \cdot 9 = 44.1
\][/tex]
6. Subtract [tex]\( 44.1 \)[/tex] from [tex]\( 90 \)[/tex]:
[tex]\[
H = 90 - 44.1 = 45.9
\][/tex]
Therefore, the height of the rock after 3 seconds is [tex]\( 45.9 \)[/tex] meters.
