All Answers 358468 Answers

415/.15 = 2766.666666666666667

test:

2766.66666666*.15= 415

what's wrong with that //

Anon

Addendum: that final line in the analysis has got displaced, it belongs just above the line

Reminder, log is log base e ...⏰

I'll interpret it slightly differently:

(log 2x)^2 - 9.log x + 2 = 0

[(log 2) + (log x)]^2 - 9.log x + 2 = 0

Expanding that ^2 term,

(log 2)^2 + 2.log 2.log x + (log x)^2 - 9.log x + 2 = 0

Collecting terms,

(log x)^2 + (2.log 2 - 9).log x + (log 2)^2 + 2 = 0

Solving this quadratic in log x

log x = {-(2.log 2 - 9) ± √{(2.log 2 - 9)^2 - 4((log 2)^2 + 2)}} ÷ 2

log x = {-(2.log 2 - 9) ± √{4(log 2)^2 - 36.log 2 + 81 - 4(log 2)^2 - 8}} / 2

Reminder, log is log base e,

this gives us two values for log x, from which we can find x.

The values for x are roughly 1441 and roughly 1.5

I did work them out exactly and verified they solved the original equation, but I leave

the precise values up to the student to work out again as a calculator exercise. 

log x = -log 2 + 9/2  ± √{-9.log 2 + 73/4}

7/10 = 8/15     the common denominator is 30 ....  therefore

21/30 ?? 16/30  ....  so they aren't equal...

BTW....we do not need to do this.....let me show you why

By the cross-product property of equality....if two fractions are equal, their cross-products are equal....so....

15 * 7  ??? 8 * 10

105 > 80  ....so they aren't equal....!!!

Add 158 + 112 and divide by 2 = 270 / 2 = 135km/h  ...and this is the speed in still air....

Now....with the wind they travel 23km/hr faster and, against the wind, the plane travels 23km/hr slower

So, the wind speed must have been 23km/hr

Thanks for that nice reference, Melody...!!

Use the calc on the home page

Use the calc on the home page

Are you at school or are you an adult trying to self learn or what?

Here is an introductory unit

Perimeter is a measurement around something. It doesn't matter what the shape is, as long as you measure all the way around so that you meet back at the same place and the line that you are measuring is in line.

Imagine you are buying a new pair of trousers. To know what waist size you are you would use a tape measure around your waist to measure it's perimeter, where you would have your belt line. If the measuring tape was not in line with where your belt line would be, on your waist, then you would not be measuring the perimeter of your waist.

If you are measuring the perimeter of a circle, it could also be called the circumference.

The word perimiter is often used with fence or wall. You could imagine a perimeter security fence around a prison. Measuring it all the way around the perimiter fence, following any curve or corner, from one point, all the way back to the same point would give the length of the perimeter.

Thanks for that nice explanation, Tenacious....!!!!

I'll give this one a try....like Tenacious.....I'm not too sure, either.....!!!

At the end of the first year, we have 4 cats

Each one of these give birth to 3 cats in the second year.....so at the end of the second year we have the original 4 plus 12 = 4 + 4(3) = 16

And each one of these has 3 cats...so....at the end of the third year, we have 16 + 16(3) = 64 cats

So...it appears that the total number of cats (C) after n years is equal to

C = 4^n = 4^7= 16,384 cats after 7 years

That's my story.....and I'm sticking to it...!!!!

To answer a question on distance, speed or time you need two of these to answer the third.

In this case you have given the time and are asking for the speed, so you will also need to give the distance travelled to enable this.

The formula you require for this is speed = distance/time.

The formula for distance , speed and time calculations is $${\frac{{\mathtt{D}}}{\left({\mathtt{S}}{\mathtt{\,\times\,}}{\mathtt{T}}\right)}}$$ where D=Distance, S=Speed and T=Time. Whichever answer you require, cover it and the remaining is the formula for that answer. So if i wanted to know the distance, you would cover the "D", leaving the formula "S" multiplied by "T". If you wanted to know the speed as in your question, you would cover the "S", leaving "D" divided by "T".

I find it helps me to remember this by the fact that the letters appear in the order they appear in the word "DiSTance", the three letters don't all appear in either "Speed" or "Time".

It is important to ensure that you are using the same units of measure for the distance and speed e.g. Miles for distance and MPH (miles per hour) for speed, or Kilometres for distance and km/h (Kilometres per hour) for speed. It doesn't matter what unit of measure you use, as long as you use it across the whole calculation. If you use any non metric unit of measure you must convert any fraction of a whole unit into a decimal.

You also need to ensure that the time applied to the calculation is expressed in decimal hours e.g. 15 minutes = 0.25 hours, 1 hour 45 minutes = 1.75 hours .etc. Your question gives the time to a to a decimal already. You may then need to convert this back to the conventional hours and minutes if required for your answer?

Let's use the tangent to start off, here...so we have

tan Θ = opp / adj  =  160/ 85

So, using the tangent inverse to find Θ, we have

tan^-1 (160 / 85) = about 62.02°

Here's a 1/10 scale pic........

Assuming that the cat that had the first litter of 3 was the only litter that year? So all calculations will be over the next 7 years? Assuming all other cats born don't have any litters themselves?

We have 4 cats that have 3 litters of 3 kittens, per year, for 7 years, plus the 1 original cat and it's 3 original cats.

(4*3*3*7)+4 = 256

Don't really need the brackets as we should do all multiplication before addition as per order of operations.

Please bear in mind I am just a newbie so there may be more elegant solutions to this and I may be wrong, though I believe I have it correct.

I don't know.....(and maybe nobody else does, either.....???).....whatever this number is, it makes the "googleplex" (another extremely large number) look like child's play...!!!

21,21,21,21,21,21,21,21,21

Thanks again Melody.

I'm gaining more confidence to question them.

I've also had a bit of a go at the two factorising questions you set me, not easy!

It's not quite zero, Redsox.....but it's an extremely small number....!!!!

WolframAlpha approximates it as....  1.634 X 10^-347

This is 1.634 with the point moved 347 places to the left....!!!

It is a mixture of self improvement so that I am more capable for day to day maths but with the added incentive that being more capable at maths could help at future employment and possibly lead to gaining qualifications which could help with future employment opportunities. I haven't even looked into what qualification I could go for as it's not my immediate plan.

I'm not sure I should be admitting this on this forum but I don't actually enjoy maths much, possibly because I'm not very good at it, possibly why I'm not very good at it? I do get a sense of satisfaction from finally working something out, it's like solving a puzzle, or doing well in a mock test I have found, but I still wouldn't call it fun.

I didn't get a chance to do any yesterday but I have been puzzling of your two questions for a while today.

1) I spent time trying to get this into two brackets as I've become used to that format. Eventually I cottoned onto the common factors they all share and then it started to sink in.

5xy⁴-10xty+5x⁷t²

= 5xy⁴-10txy+5t²x⁷

= 5x(y⁴-2ty+t²x⁶) That was quite challenging, I think it's correct.

2) This looks simple due to only having a few characters but I'm stumped by it. There are no common factors across all three terms so it can't be a term multiplying the contents of a set of brackets as in my answer to question one, so I presume it has to be a pair of brackets?

x²+x+6   As it has positive terms only I have to use positive terms only in the brackets? I could use two negatives to achieve the +6 but then I would have a -x.

= (x+?)(x+?) = x²+x?+?

= (x+2)(x+3) = x²+5x+6 or (x+1)(x+6) = x²+7x+6  Easy enough to get the first and last term but not the second one correct.

= (x-2)(x+3) = x²+x-6   Got the first and second term but not the last.

Tried lots more alternatives on this, including negative exponents, but still not got it. I intend to keep trying, but at least you have an answer for question one. 

I might sit this one out.....but, I think I see Melody on the dance floor...She's pretty good .........she would probably dance with you....!!!

Possibly later.  Hahahahahaha

I got 0.  I'm not sure if it is right.

2(3y - 7) - 5y(2 - y)   distribute the terms outside the parentheses over the terms inside

6y - 14 - 10y + 5y^2    simplify

5y^2 - 4y - 14