A. calculate the volume of the solid of revolution created by rotating the curve y = 3 + 3 exp(-5 x) about the x-axis, for x between 2 and 4. volume : 56.55 b. the equation of a circle of radius r, centered at the origin (0,0), is given by r^2 = x^2 + y^2 rearrange this equation to find a formula for y in terms of x and r. (take the positive root.) what solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -r and r suppose we wanted to set the following integral so that v gives the volume of a sphere of radius r v = integral a to b f(x) dx what would a, b and f(x) be? a=b=f(x)=carry out the integration, and calculate the value of v in terms of r. v=

A) The volume of solid is 18π cubic unit.

B) The volume of sphere is

    a = -r , b = r , and

Solution A)

The given curve, rotate about x-axis between 2 to 4.

Please find attachment for solid figure or rotation.

Using disk method to find the volume rotation about x-axis

where, a = 2, b= 4 , and dx is thickness of disk.

Hence, the volume of solid is 18π cubic unit

Solution B)

The equation of circle of radius r and centered at origin (0,0).

The solid form is sphere of radius r.

Using disk method, to find volume of solid

where, a = -r, b = r , and dx is thickness of disk.

Hence, the volume of sphere is

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

happy to

pls mark as brainliest