Use ANT's hint to write a general formula for the sum, then prove it works by induction.

Bob

]]>So the roots are

one of them is *ɑ*, the other is *β*. Since the question doesn’t say which is which, you may as well take your pick. Now use De Moivre’s theorem.

If the discount is 10% then how it costs 0.9x?

If you take 10% off the price, you'll be left with 90% to pay.

3x/10 is correct. Then rearrange the formula I gave:

This answer will be in hours so you'll need to convert to minutes.

Bob

]]>There's lots on percentages here:

https://www.mathsisfun.com/numbers/perc … hange.html

and there are links to other useful pages.

I have looked at all the questions. But you have got to learn how to do them so I'm not going to give you answers to them all.

I suggested a method that would work for them all. Call one of the amounts x.

eg. Q1

Call the third amount x.

Then the first is 1.20x and the second is 1.50x.

Now you can work out the answer. Here, like the one I showed before, the 'x' cancels out of the final answer.

Bob

]]>(note that the angular velocity of the minute hand is 2*π*/(60×60) radians per second). Differentiate:

Set to to 0:

This equation can’t be solved analytically; using Wolfram|Alpha, I get *t* ≈ 493 seconds = 8 minutes 13 seconds, i.e. the insect is at its highest position at 12:08:13.

Check that d²*h*/d*t*² < 0 so that this is indeed a maximum value.

It is indeed 23.678.

Cheers!

]]>Welcome to the forum.

Try here:

Bob

]]>If you put *x* = 0, you’ll find that the first term involves the expression 0⁰. Rather than saying the formula is invalid because 0⁰ is undefined, we happily let 0⁰ = 1 anyway.

Nice method

Bob

]]>Quadratics

Polynomials

Radicals

Rationalizing Denominators

Geometric+Arthematic sequences

All of these should be basic. Quadratics shouldn't need to use the quadratic formula like yours did. New problem 2:

What value of x solves this equation?

]]>

I have posted a solution to your limit problem, if you would like to check your other thread.

]]>