Aregion in the plane is bounded by the graph of y=1/x, the x-axis, the line x=m and the line x=3m, m> 0. the area of this region:
a) is independent of m
b) increases as m increases
c) decreases as m increases
d) decreases for all m< 1/3
e) increases for all m< 1/3

The area of plane is independent of m, A=log 3

A is correct

Step-by-step explanation:

A region in the plane is bounded by the graph of

x-axis

Line: x=m and x=3m

Please find the attachment for figure.

Area under the curve = integrate the curve from m to 3m

Using log property: log a - log b = log(a/b)

Hence, The area of plane is independent of m.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi