Answer:
-2.92178
Step-by-step explanation:
Given the function 
The average,A is calculated using the formula;
![A=\frac{1}{b-a}\int\limits^a_b F(x)\, dx \\\\A=\frac{1}{7-1}\int\limits^7_1 3x \ Sin \ x\, dx \\\\\\=\frac{3}{6}\int\limits^7_1 x \ Sin \ x\, dx \\\\\#Integration\ by\ parts, u=x, v \prime=sin(x)\\=0.5[-xcos(x)-\int-cos(x)dx]\limits^7_1\\\\=0.5[-xcos(x)-(-sin(x))]\limits^7_1\\\\=0.5[-xcos(x)+sin(x)]\limits^7_1\\\\=0.5[-6.82595--0.98240]\\\\=-2.92178](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7Bb-a%7D%5Cint%5Climits%5Ea_b%20F%28x%29%5C%2C%20dx%20%5C%5C%5C%5CA%3D%5Cfrac%7B1%7D%7B7-1%7D%5Cint%5Climits%5E7_1%203x%20%5C%20Sin%20%5C%20x%5C%2C%20dx%20%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7B3%7D%7B6%7D%5Cint%5Climits%5E7_1%20x%20%5C%20Sin%20%5C%20x%5C%2C%20dx%20%5C%5C%5C%5C%5C%23Integration%5C%20%20by%5C%20%20parts%2C%20u%3Dx%2C%20v%20%5Cprime%3Dsin%28x%29%5C%5C%3D0.5%5B-xcos%28x%29-%5Cint-cos%28x%29dx%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-xcos%28x%29-%28-sin%28x%29%29%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-xcos%28x%29%2Bsin%28x%29%5D%5Climits%5E7_1%5C%5C%5C%5C%3D0.5%5B-6.82595--0.98240%5D%5C%5C%5C%5C%3D-2.92178)
Hence, the average of the function is -2.92178
Answer:
A) There are 8 possible combinations
Step-by-step explanation:
(1 x 4) + (1 x 4) = 8
The function rule I will be using is this:
Four ordered pairs that could represent this linear function are:
(0, 5)
(1, 7)
(2, 9)
(3, 11)
Answer:
y = 37/5x + 9
Step-by-step explanation:
The points are not plotted on a single straight line, so I will find the general slope using the first and last point on the graph.
(5, 46) & (10, 83)
slope-intercept form: (y₂ - y₁) / (x₂ - x₁)
(83 - 46) / (10 - 5)
Simplify.
(37)/(5)
Your slope is 37/5.
y = 37/5x + b
To find b, plug in a point to x and y.
46 = 37/5(5) + b
46 = 37 + b
b = 9
Your equation is: y = 37/5x + 9
Check by plugging in the other point.
83 = 37/5(10) + 9
83 = 74 + 9
83 = 83
Your equation is correct.
Hope this helps!
Answer:
Step-by-step explanation:
Area of rectangle = length x width
Area of square = side x side
Given: Dimension of rectangular wall: 8 feet high and 30 feet wide
Area of rectangular wall = 8 feet x 30 feet = 240 ft²
Height of square wall = 9 feet
Area of square wall = 9 x 9 ft² = 81 ft²
Total area need to paint = 240 ft²+ 81 ft² = 321 ft² > 250 ft.²
i.e. Molly does not have enough p[aint to cover both walls.
