30:30 is impossible as the angles don't add up to 90.

45:45 won't work as the opposite and adjacent would be equal in this case.

30:60 won't work as the opposite and adjacent are in the ratio root 3 : 1

Bob

]]>The first method is technically correct.

It is always advisable to use this method.

The second method may give more of less the same value.

This is for the beginners.

]]>they both start marking a paper at 11:00 AM, what is the first time they will finish marking

a paper at same time?

Question 2: Of two kinds of alloy , silver and copper are contained in one in the ratio of 5:1 and in the other in the ratio of 7:2 . What weights of the two alloys should be melted and mixed together so as to make up a 5 lb mass with 80% of silver?

Question 3 :An alloy contains copper and zinc in the ratio of 5:3 and another alloy contains copper and tin in the ratio 8:5 . If equal weights of both alloys are melted together find the weight of tin in the resulting alloy per kg?

Question 4 : The average daily temperature from 9th January to 16th January (both inclusive) was 38.6 degree and that from the 10th to 17th January (inclusive) was 39.2 degree . What was the temperature on 17th January?

]]>Illustration:

LCM of 0.24, 1.2 and 1.92

To find LCM of decimals, we must change the smallest number into whole number by multiplying it by any friendly number i.e. 10, 100, 1000, 10000 etc.

So, we will multiply 0.24 by 100 to make it a whole number (24).

Here, we have multiplied the smallest number by 100 so, the other two numbers will also be multiplied by hundred. Thus, we will get 24, 120 and 192.

Now, we will take LCM of all three numbers. We will get 960.

As, we had multiplied the numbers by 100, so now we will divide the obtained LCM by hundred.

So, we will get 9.6 which is our answer.

*Another Method:*

*Its just like finding the LCM of 24, 120 and 192*.

.

So it would be

.Now, you just move the decimal place back two places.

Required answer : 9.6!

]]>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

]]>