Melody

answered.

Get cos(theta) in terms of x

Get sin(theta) in terms of y

then my hint is     sin^2(theta)+cos(^2(theta)=1

The volume of a cylinder of height 11 inches and radius r inches is given by the formula V=11πr2.

Suppose that the radius is expanding at a rate of 0.6 inches per second. How fast is the volume changing when the radius is 2.3 inches? Use at least 5 decimal places in your answer.  ____???cubic inches per second

\(V=11\pi r^2\\ \frac{dV}{dR}=22\pi r\)

\(\frac{dr}{dt}=0.6\)

\(\frac{dV}{dt}=\frac{dV}{dr}\times \frac{dr}{dt}\\ \frac{dV}{dt}=22\pi r\times 0.6\\ \frac{dV}{dt}=13.2\pi r\\ When\;\;r=2.3\; inches\\ \frac{dV}{dt}=13.2\pi *2.3\\ etc \)

LaTex:

V=11\pi r^2\\
\frac{dV}{dR}=22\pi r

\frac{dr}{dt}=0.6

\frac{dV}{dt}=\frac{dV}{dr}\times \frac{dr}{dt}\\
\frac{dV}{dt}=22\pi r\times 0.6\\
\frac{dV}{dt}=13.2\pi r\\
When\;\;r=2.3\; inches\\
\frac{dV}{dt}=13.2\pi *2.3\\
etc

Try proof reading your question and not just posting garbage.

Thanks Kadjaye   

No, but I will give you a good hint.

Multiply both sides by the lowest common denominator (which is 12)

I do not know if I understand the question but if the biggest difference between the pairs is 3 then the pairs could be

1,4

2,5

3,6

7,10

8,11

9,12

13,16

14,17

15,18

19,22

20,23

21,24

25,28

26,29

27,30

31,34

32,35

33,36

37,40

38,39

19*3+1 = 58

So I get the same 'guess' answer as guest does.   

You have done a lot of work there guest!

Good going. I'd give you more points if I could.          

(I have not checked it properly but it looks impressive)   

Just thinking about it logically I can see that this will happen between 1:35 and 1:40 So any calc I do can be checked against this.

The hour hand starts 30 degrees past the hour and the minute hand starts on the hour.

After 1 minute the hour hand travels 0.5 degrees and the minute hand travels 6 degrees

so

After x minute the hour hand travels 0.5x degrees and the minute hand travels 6x degrees

the hour hand starts on the 1 so it has that 30 degrees 'head start'

The angle between for the first half hour of so will be  6x-(30+0.5x) and we want that equal to 180

Solve the equation and we get x= \(38\frac{2}{11}\;\;minutes\)

So at   \(38\frac{2}{11}\;\;minutes\)  past 1 the hands will be exactly opposite each other.

(just as our guest already determined. - thanks guest)