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:
The histogram of the data is attached below.
Step-by-step explanation:
A histogram is a demonstration of statistical data that uses bars to illustrate the incidence of data values in successive numerical intervals of same size. In the most basic form of histogram, the independent variable is marked along the x-axis and the dependent variable is marked along the y-axis.
The data provided is:
X Frequency
1 12
2 3
3 7
4 9
5 18
6 14
The histogram of the data is attached below.
Answer:
i would guese c
Step-by-step explanation:
Answer:
(6,2)
Step-by-step explanation:
Variable Definitions:
x= the number of commercials
y= the number of movies
Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:
50x+150y=600
Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.
x=3y
Write System of Equations:
50x+150y=600
x=3y
Solve for y in each equation:
1) 50x+150y=600
150y=−50x+600
y=-1/3x+4
2) x=3y
y=1/3x
The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:
Emily's songs were played on 6 commercials and 2 movies.
