Hello!!
Ok so if 8 laps is 1 mile, then 3/8 of a mile is 3 laps. Think if 8laps is 1 mile then each lap represents 1/8 mile so 3/8 mile is equal to 3 laps!
Hope this helps u understand! Any questions please ask!! Thank you so much!!
Looks like the given curve is
5<em>xy</em> + <em>z</em>⁴<em>x</em> - 3<em>yz</em> = 3
Differentiate both sides with respect to <em>x</em> :
5<em>y</em> + 4<em>z</em>³<em>x</em> ∂<em>z</em>/∂<em>x</em> + <em>z</em>⁴ - 3<em>y</em> ∂<em>z</em>/∂<em>x</em> = 0
Solve for ∂<em>z</em>/∂<em>x</em> :
(4<em>z</em>³<em>x</em> - 3<em>y</em>) ∂<em>z</em>/∂<em>x</em> = - (5<em>y</em> + <em>z</em>⁴)
∂<em>z</em>/∂<em>x</em> = - (5<em>y</em> + <em>z</em>⁴) / (4<em>z</em>³<em>x</em> - 3<em>y</em>)
At the point (1, 1, 1), this derivative is
∂<em>z</em>/∂<em>x</em> (1, 1, 1) = - (5 + 1) / (4 - 3) = -6
100 is the y intercept so its graohed at (0,100)(y-axis) and it goes up every 1/55
