Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. the shape of the mirror can be modeled by (x-2)^2=10(y-3), where x and y are measured in inches. where is the focus of the flashlight?
a. (–2, –0.5)
b. (2, –5.5)
c. (2, 5.5)
d. (5.5, 2)

(2, 5.5)

Step-by-step explanation:

The standard form of parabola is :

---1

where the focus is  

Now we are Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source.The shape of the mirror can be modeled by:

Now compare it with 1

Now Focus  is  

So, the focus of the flash light =

                                                   =

Hence  the focus of the flashlight is  (2, 5.5)

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

its perfect good job honey

step-by-step explanation:

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