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
Mean: The average or the center of the value. To find this, you add up all the numbers and divide by how many numbers there are.
Example: 3, 4, 5
3+4+5 = 12.
There are 3 numbers.
12/3 = 4. The mean is 4
Median: Median means the middle value. You place the numbers in order and locate the middle value.
Example: 5, 4, 3 -> 3,/ 4,/ 5. Middle number 4.
Mode: Place the numbers in order then count how much each number appears. The number that appears the most repeatedly would be the mode.
Example: 3, 4, 4, 4, 5, 5.
The mode would be 4.
Range: Locate the highest and the lowest values of the given set and subtract the smallest to the largest.
Do you know where to start now?
Multiply the number by 75%
