Answer:
Step-by-step explanation:
Yay graphs!!!!!!
Okay so as you should know, the structure of a linear equation is y = mx + b.
B is the y-intercept
so the first thing to do is mark the coordinates (0,1) as the y-intercept
Now the slope is 1/4 x
this is also known as rise/run
A simpler way to do that is from (0,1) move up 1 and over four and place a point there
The coordinate should be (4,1)
Then draw a line through the two points
Answer: 24 square units
Step-by-step explanation:
It appears the shaded area of the rectangle is half of the rectangle's area. This means if we find the area of the rectangle and divide it by 2 we will know the area of the shaded portion.
The formula for the area of a rectangle is 
Where
l is the length (8 for this)
w is the width (6 for this)
A is the area
However, since we are finding half the area we will divide lw by 2
Sub the values into the formula
We can't necessarily draw it out for you unless someone links something.
Answer:
74 feet and 6 feet
Step-by-step explanation:
Mentioned that
The Length of the dog park is = (8x + 2)............(i)
And,
The Width of the park is = (2x -12)..................(ii)
Perimeter = 160 feet
Now here we use the perimeter formula which is
Perimeter is
= 2 (length + width)
160 = 2 (8x + 2 + 2x - 12)
160 = 2 (10x - 10)
160 = 20x - 20
180 = 20x
x = 9
Now put the x value into the equation 1 and equaton 2
For the equaton 1, the length us
= 8x + 2
= 8(9) + 2
= 74 feet
And, the width is
= 2x - 12
= 2(9) - 12
= 18 - 12
= 6 feet
Answer:
-9π
Step-by-step explanation:
∫c (4y dx + 2xy dy)
= ∫∫ [(∂/∂x)(2xy) - (∂/∂y)(4y)] dA, by Green's Theorem
= ∫∫ (2y - 4) dA
Now convert to polar coordinates:
∫(r = 0 to 3) ∫(θ = 0 to 2π) (2r sin θ - 4) * (r dθ dr) --- first integration
= ∫(r = 0 to 3) (-2r cos θ - 4θ) * r {for θ = 0 to 2π} dr
= ∫(r = 0 to 3) -2πr dr
= -πr² {for r = 0 to 3}
= -π(3²) - -π(0)²
= -9π
