I NEED MORE OF AN UNDERSTANDING ON HOW TO DO THIS!!!!

A semielliptic archway has a height of 20ft. and a width of 50ft. as shown in the figure, can a truck 14ft. high and 10 feet wide drive under the archway without going into the other line?

Question

I NEED MORE OF AN UNDERSTANDING ON HOW TO DO THIS!!!!

A semielliptic archway has a height of 20ft. and a width of 50ft. as shown in the figure, can a truck 14ft. high and 10 feet wide drive under the archway without going into the other line?

anonymous · Answer

can you help me

turingtest · Answer

what is the equation of this ellipse
can you find it?

anonymous · Answer

its x^2/625 + y^2/400=1

turingtest · Answer

correct, and here it is
just consider the top half|dw:1331429100637:dw|now we want to know how the shape of our truck fits in on this graph...
if we center the truck at x=0, it will stick out to x=-5 and x=5, because it is ten wide...
we know how high the truck is, so if we know how high the tunnel is at x=5, we will be able to compare the two

anonymous · Answer

okay @TuringTest

turingtest · Answer

|dw:1331429282485:dw|knowing the height of the tunnel at x=5 means solving for y of x=4 in the equation
so$$\frac{5^2}{50^2}+\frac{y^2}{20^2}=1$$solve for y