Answer:
4 feet
Step-by-step explanation:
Since the whispering gallery is 15 feet high and 60 feet wide, it forms an ellipse with major axis along the width of the gallery and minor axis along the height of the gallery.
Using the equation of an ellipse with major axis along the x-axis, we have
x²/a² + y²/b² = 1 where a = midpoint of the width = 60/2 = 30 feet and b = 15 feet.
c² = a² - b² where c = focus of the ellipse.
So, c² = a² - b²
= 30² - 15²
= 900 - 225
= 675
c = ±√675 = ±25.98 feet
So, the coordinate of the focus is thus (0, ±c) = (0, ±25.98) and the coordinate of the vertex is (0, ±a) = (0, ±30)
So, the distance between the foci and the vertex is the distance from the wall at which each of them should be positioned at the foci.
So, d = a - c
= 30 ft - 25.98 ft
= 4.02 feet
≅ 4 feet
Answer : Kamala
Speed = distance/time
For John : speed = 30/1.5 = 20 km/h
For Kamala : speed = 42/2 = 21 km/h Thus Kamala has a greater average speed than John.
Hope it helped!
Answer:
46 1/2 miles
Step-by-step explanation:
Given:
Distance = 15 1/2 miles
Time = 1/3 hour
Distance =?
Time = 1 hour
Distance : time
15 1/2 miles : 1/3 hour = ? miles : 1 hour
31/2 miles ÷ 1/3 bout = x miles / 1 hour
31/2 × 3/1 = x / 1
93 /2 = x
x = 93/2 miles
= 46 1/2 miles
Therefore, the bus will travel 46 1/2 miles in an hour
Find plane Π parallel to 5y-5x-5z=4 containing point p=(2,3,4)
Any plane parallel to 5y-5x-5z=4 has the form 5y-5x-5z=k, or on simplification, y-x-z=k.
Since p lies in the plane, the coordinates of p must satisfy y-x-z=k, or
k=3-2-4=-3
=>
π : y-x-z=-3
equivalently,
π : 5y-5x-5z=-15
Cross multiply
5*27=135
3*x=3x
set equal to one another
3x=135
solve for x
135/3=x
45=x
x=45 minutes
