Find the lateral (side) surface area of the cone generated by revolving the line segment y equals seven halves x , 0 less than or equals x less than or equals 5, about the x-axis. Check your answer with the following geometry formula. Lateral surface areaequalsone half times base circumference times slant height

Step-by-step explanation:

Let's use the integral formula for the surface area of revolution of the function y(x) around the x-axis, which is:

and which in our case, we can obtain the following:

Recall as well that , which gives us the limits of integration:

If we compare it with the geometry formula:

Lateral surface of cone =

which is exactly the expression we calculated with the integral.

2

step-by-step explanation:

0 and 5 minutes

step-by-step explanation:

given that one morning eight buses arrive late by the number of minutes given below:

0 8 2 6 9 2 0 7 8

write these in ascending order

0   0 2 6 7 8 8 9

in the afternoon two more buses arrive at the bus stop say by x and y minutes late.

total number of buses = 10

median = average of 4th and 5th after arranging in ascending order

since 4th entry is 6, the values of x and y should be below 6

also given 0 is the mode so either x or y or both should be 0 because then only 0 gets the maximum frequency and hence mode

thus we have

0 0 0 2 6 7 8 8 9 and another unknown entry which is below 6.

since median is 3.5, we have the unknown entry to be 5 only because then only median =( 2+5)/2

thus the after noon buses were late by 0 and 5 minutes.