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i have to figure out how to get out of here. i managed to cut a hole behind the paper on the wall i might be able to fit through
the diameter of the hole is 28 inches, meaning the radius is 14 inches. The walls are 24 inches thick. the other end of the hole has a radius of 7 inches.
i can use area under the curve and revolutions to figure out the volume of the cylinder to see if i can fit.
∫0-23 ℼ(7/24x+14)^2this equation can represent the area when revolved around the x axis
5
The total area when revolved is 1836 feet, and should be a big enough hold to fit through.
10
the line can be revolved to find the volume of the hole to see if i can fit. the line can b represented by y=7/24x+14
15
20
25
I made it outside, but now i need to figure out how to avoid the moving spot light
the light that is 5 meters high moves on the ground at a rate of 0.5 meters per second. at its furthest point, the beam of light is 6 meters. I need to find the speed that the light is moving, and can use related rates to do so
x^2+y^2=z^22x dx/dt + 2y dy/dt = 2z dz/dt2(sqrt11)(0.5) + 2(5)(0) = 2(6)(dz/dt)sqrt11=12dz/dtdz/dt= 11m/s
The scenario can be represented by a right triangle. The missing side length can be found using pythagorean theorem. Then you can use the equation to find the missing rate.
5^2+b^2=6^225+b^2=36b=sqrt11m
6m
?m/s
0.5m/s
5m
0m/s
since i was able to find out the spotlights moved at 11m/s, i was able to avoid them and get out!

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