For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.
So, all we have to do is substitute θ=45° to the function given.
A = 16 sin 45° ⋅ (cos 45° + 1)
The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.
A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8+8√2
A = 19.31 square inches
Answer:
choice a
Step-by-step explanation:
angle 45 means, its a isosceles triangle.
so y = √3
x^2 = 3+3= 6
x = √6
In this problem, it will be helpful to know the vertex form of a parabola, which is listed below:
is a constant which helps to determine whether the parabola opens up or down. If 
, then the parabola opens downward and if 
, the parabola opens upwards
is the vertex of the parabola
By looking at the graph, we can first see that the graph opens downwards, meaning that . Thus, choices C and D are not valid. Now, let's use the vertex of the parabola to complete the equation.
The vertex of this parabola is (-1, 3), as shown by the graph. When we substitute this into our formula, we get:
The answer is a, 
.
Answer:
$3
Step-by-step explanation:
