Answer:
V = 91π / 6
Step-by-step explanation:
When we revolve the region about y = 2, we get a cylindrical shape on its side. If we slice the shape into concentric shells, then each shell will have a radius of 2 − y, a thickness of dy, and a length of 7 − x. The volume of the shell is:
dV = 2π r h t
dV = 2π (2 − y) (7 − x) dy
x = 7y², so:
dV = 2π (2 − y) (7 − 7y²) dy
dV = 14π (2 − y) (1 − y²) dy
dV = 14π (2 − 2y² − y + y³) dy
The total volume is the sum of all the shells from y=0 to y=1.
V = ∫ dV
V = ∫₀¹ 14π (2 − 2y² − y + y³) dy
V = 14π (2y − ⅔ y³ − ½ y² + ¼ y⁴) |₀¹
V = 14π (2 − ⅔ − ½ + ¼)
V = 91π / 6
Answer: The answer is (B) 2x + 3(3x – 5) = 51
.
Step-by-step explanation: We are given three options and we are to select which choice shows the result of substituting 3x – 5 into the second equation for y.
So, y = 3x - 5.
Since the standard form of a linear equation i two variables is ax + by = c, so the second equation as given in the options must be of the form 2x + 3y = 51.
If we substitute y = 3x - 5, then this equation becomes
2x + 3(3x - 5) = 51.
Thus, (B) 2x + 3(3x – 5) = 51 is the correct option.
The answer is y=1/4x because the y-intercept is zero and the slope is 1/4.
Answer:
2
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. Since midpoints will be involved, use multiples of 2 to name the coordinates for B, C, and D.
Answer:
czbjc,bxjc,bdhcjdgbch
Step-by-step explanation:
good day