A headlight is being constructed in the shape of a paraboloid with depth 4 inches and diameter 5 inches. Determine the distance that the bulb should be from the vertex in order to have the beam of light shine straight.

d = 0.39 inch

Step-by-step explanation:

Given data:

Diameter (x) = 5inch

Depth (y) = 4 inch

Distance (d) = ?

Using the parabola formula to find the distance d, we have

x² = 4dy

where x = 5/2 = 2.5 and y = 4

Substituting, we have

2.5² = 4 * d* 4

6.25 = 16d

d = 6.25/16

d = 0.39 inch

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950