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?

F(2, 11/2)

Step-by-step explanation:

The expression:

(x-2)² = 10(y - 3)

can be rewritten in the vertex form as follows:

(x-2)² = 10y - 30

(x-2)² + 30 = 10y

1/10(x-2)² + 3 = y

General vertex form is:

y = a(x-h)² + k

then, the vertex is locate at (h, k). In this case the vertes is (2, 3), and a = 1/10

The focus of a parabola is located ar F(h, k+p), where p = 1/(4a). Replacing into these equations:

p = 1/(4*1/10) = 5/2

F(2, 3+5/2) = F(2, 11/2)

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500