An architect has designed two tunnels. Tunnel A is modeled by x² + y² + 30x + 56 = 0, and tunnel B is modeled by x² 30x + 16y-95= 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels. Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work.
An architect has designed two tunnels. Tunnel A is modeled by x² + y² + 30x + 56 = 0, and tunnel B is modeled by x² 30x + 16y-95= 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels. Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work.
Chapter8: Analytic Geometry
Section8.1: The Ellipse
Problem 6TI: Express the equation of the ellipse given in standard form. Identify the center, vertices,...
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