4. Volume of cylinder with radius = 4 m.

Height = 8 m.

.

Solution : Volume = 402.1248 cubic meters.

Rounded to 402 cubic meters.

Option (d) is correct.

5. Volume of a cylinder with diameter 21 centimeters and height 15 centimeters.

Here, diameter = 21 centimeters, radius = 10.5 centimeters.

cubic centimeters.

Option (c) is correct.]]>

Anyway, what I wanted to say was: is it possible to ahve some kind of "difficulty level" along with the exercises? I've browsed to the forum and have found almost only things I don't even understand. Not things I can't solve, but things I don't understand at all... I've come here with a rusty high school level of mathematics as to get better, and now I just feel lost. Sorry for having suh a low level, but I'm here to solve that issue!

]]>I made a video explanation here, if Zeeshan 01 would like to have a look.

]]>There are two stages to this problem. I think you have done the first but I'll say anyway.

This is a product of two functions so use the product rule:

You can combine the trig functions into a single trig function using the compound angle formulas. You want a cosine so I'll use

To make the derivative look like the right hand side here:

Hope that helps,

Bob

]]>Welcome to the forum.

Looks like you've got these sorted ; I agree with all your answers.

Bob

]]>Welcome to the forum.

I've been hoping that someone would post an answer to this and I could learn too. No such luck

So I'm having a go myself. Please note: I've never done this before, so what follows may be rubbish. Please comment …. ask for clarification … tell me why it's wrong etc. Maybe between us, we can arrive at the correct answer. And oh yes … your English is good.

So let's work with 3D coordinates with the x-y plane horizontal and z going straight up. Further, let's make the sphere have unit radius (cannot see any harm in that) and centred on the origin, O.

If P is one point of the tetrahedron, then we can specify its position using spherical coordinates theta and phi as shown here: https://en.wikipedia.org/wiki/Spherical … ate_system And let P' be the point in the x-y plane below P.

Now, what would be helpful is to have a formula for the volume of a tetrahedron in terms of theta and phi but I cannot find one. Plenty of internet pages giving the formula in vector terms such as https://math.stackexchange.com/question … ot-product

and as a determinant https://stackoverflow.com/questions/986 … n-4-points

I could also expand either into a large algebraic formula but it would take ages to enter all the LaTex so you'll have to ask nicely if you want this.

phi can take any random value from 0 to 2pi and theta any from 0 to pi.

So you can construct your function with 8 variables and there it is. Hhhmmmm.

Bob

]]>]]>

Sorry, but I do not understand what you are asking. Please post the whole question.

Bob

]]>Zeeshan 01 wrote:

Integration of (1/(1+sinx+cosx)) dx by letting tanx/2=z

So that's what I did.

The alternative method of post 4 does not use z at all.

You now have the presence of a function and it's derivative, so it is directly integrable as ln(function) .

Bob

]]>Try this:

https://www.mathsisfun.com/data/functio … (log (3))

Bob

]]>I used the cosine rule thus:

Bob

]]>