Question

A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle θ. The area A of the opening may be expressed as the function: A(θ) = 16 sin θ ⋅ (cos θ + 1). If θ = 45°, what is the area of the opening?

Answer 1

The answer choices are
4.8 in^2
9.0 in^2
19.3 in^2
20.8 in^2
I think it is 19.4 in^2

Answer 2

*19.3

Answer 3

correct,but can you show me your work?

Answer 4

I converted the 45 degrees to radians using 45 times pi over 180. This got me 16 sin pi over 4 (cos pi over 4 + 1). Then, pi over 4 is 1 over the square root of 2. If you plug that in you get 16(1/sqrt2(1\sqrt2+1) and this simplifies to 8(1 + sqrt2) which is 19.3.

Answer 5

(10.06 MC)
Functions f(x) and g(x) are shown below:

f(x) g(x)
f(x) = 3x2 + 12x + 16
g(x)=2sin(x-pie)
Using complete sentences, explain how to find the minimum value for each function and determine which function has the smallest minimum y-value

Answer 6

@jfernandes

Answer 7

PLZZZZZ someone help me

Answer 8

minimum value sin theta =-1
minimum value of g(x)=-2

Answer 9

f(x)=3x^2+12x+16
=3(x^2+4x)+16
=3(x^2+4x+4-4)+16
=3(x^2+4x+4)-12+16
=3(x+2)^2+4
minimum value =?