A searchlight is shaped like a paraboloid of revolution. If the light source is located 4 feet from the base along the axis of symmetry and the opening is 20 feet​ across, how deep should the searchlight​ be?

The searchlight should be 6.25ft deep

Step-by-step explanation:

Given

Required

The depth of the searchlight

implies that the search light span 10 units to either side of the x-axis

implies that the search light span 4 units to the y-axis

The attached image illustrates the revolution.

From the attached image, the endpoints of the searchlight is:

The depth (a) of the search light is calculated using:

Make a the subject

Substitute -10 or 10 for x and 4 for y

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752