All Answers

-1

a + b=14,
a^3 - b^3 = 81, solve for a, b

Use substitution to get:

a≈7.27537 and b≈6.72463 {Real solution}
a≈6.86232 - 12.1267 i and b≈7.13768 + 12.1267 i {Imag. solution}
a≈6.86232 + 12.1267 i and b≈7.13768 - 12.1267 i {Imag. solution}

GuestJul 14, 2023

This simplifies to 5/4^98.

GuestJul 14, 2023

Very well, believe what you must. But eventually, this website will fall into decay from lack of management and lack of new users. Then, it will be overwhelmed by spammers and hackers and turn into a faulty redirect to spam sites, a reminder that quality standards are important for the survival of a Q&A platform.

GuestJul 14, 2023

-1

In 1953, Bonner and Frascella estimated that the volume of a single amoeba was 4/3 * pi * (4 micrometer)^3 = 256 micrometer^3.

The volume of a slug was estimated to be 2.74 * 10^8 micrometer^3.

Therefore, the number of amoeba in a slug was estimated to be 2.74 * 10^8 / 256 = 105,000.

In 1998, Bonner estimated that the volume of a single amoeba was 4/3 * pi * (8 micrometer)^3 = 512 micrometer^3.

The volume of a slug was still estimated to be 2.74 * 10^8 micrometer^3.

Therefore, the number of amoeba in a slug was estimated to be 2.74 * 10^8 / 512 = 53,000.

So, Bonner's new estimate was 53,000 amoeba in a single slug.

GuestJul 14, 2023

The area of the circumcircle of a triangle is given by:

K = r * s

where r is the circumradius of the triangle and s is the semiperimeter of the triangle.

The area of the incircle of a triangle is given by:

k = r * s * _S_

where r is the inradius of the triangle, s is the semiperimeter of the triangle, and S is the semi-sum of the triangle's side lengths.

In this case, the semiperimeter of the triangle is s = (26 + 10 + 24) / 2 = 30.

The semi-sum of the triangle's side lengths is S = (26 + 10 + 24) / 2 = 30.

The circumradius of the triangle is r = s / 2 * S = 30 * 30 / (2 * 30) = 13.

The inradius of the triangle is r = s / (2 * S) = 30 / (2 * 30) = 4.

Therefore, the area of the circumcircle is K = 13 * 30 = 390pi, and the area of the incircle is k = 4 * 30 * 30 / (2 * 30) = 120pi.

Therefore, x - y = 390pi - 120pi = 270pi.

GuestJul 14, 2023

you are 100% right

GuestJul 14, 2023

-1

The function floor(x) + floor(2x) + floor(3x) + floor(4x) takes on different values for 0 <= x <= 1 if and only if the fractional part {x} of x satisfies 0 <= {x} < 1/4. The different values that {x} can take on in this range are 0, 1/4, 2/4, 3/4, and 1. Therefore, the function floor(x) + floor(2x) + floor(3x) + floor(4x) takes on 1 + 4 = 5 different values in the range 0 <= x <= 1.

GuestJul 14, 2023

-2

This is so true. The website is going down.

Actually it’s not ...well, maybe in your wet-dream fantasies, but not in any existent reality –virtual or otherwise. Long after you quit giving a damn about this Forum, it will still be here. I know this because...

A Funny Thing Happened on the Way to the Forum...

--. .-

GuestJul 14, 2023

-4

-3

So.... Why is this Verrrry in—ter—esting! .........???

The originator of this thread is none other than the Forum’s Mr. BB –The Bullshit Bug.

--. .-

GingerlockHolmesJul 14, 2023

-3

For those of you wondering about CPhill and others ...

Verrrry in—ter—esting! ....

Stay tuned to find out why ....

--. .-

GuestJul 14, 2023

If you took 2 seconds to try out some cases you would get it immediately. Grow up and do it yourself.

GuestJul 14, 2023

Some examples I found:

Please give me all the answers i too lazy to spend 5 seconds searching on google: https://web2.0calc.com/questions/find-the-exact-values_1

ChatGPT: https://web2.0calc.com/questions/help-please_44203

Insidiously incorrect: https://web2.0calc.com/questions/i-need-help-with-algebra_1

GuestJul 14, 2023

This is an example of a chat-gpt answer. Does it sound like chatGPT? Yes. Does ZeroGPT think it is? Yes. Is it correct? No. Is moderation going to do anything? No. "B-but we don't have any pwoof!!" I don't care. It's incorrect anyhow, and should be deleted. Of course, we are keen on protecting the egos of anonymous users more than the quality of the site.

GuestJul 14, 2023

And this, is an example of someone who does NO RESEARCH beforehand and expects to be spoonfed the answers. You could literally google search it. Put in some more effort. We're not going to baby you.

GuestJul 14, 2023

This is one of the more insidious sh*t answers, they give some "helpful" information then leave you with nothing. B*tch, there is no nice method to solve that third degree polynomial. Do better.

GuestJul 14, 2023

-4

a*a*a-b*b*b=81

a=14-b

we substitute-

(14-b)^3-b^3=81

simplify

2744-588b+42b^2-2b^3=81

then just isolate and solve.

GuestJul 14, 2023

-3

The sum of the coefficients of the expansion of (5a/3-2b/3)^10 is 1024.

The binomial theorem tells us that the sum of the coefficients of the expansion of (x+y)^n is given by 2^n. In this case, x = 5a/3 and y = -2b/3, so the sum of the coefficients is 2^10 = 1024.

Here is a proof of the binomial theorem:

(x+y)^n = nC0x^n + nC1x^(n-1)y + nC2x^(n-2)y^2 + ... + nCy^(n-1)x + y^n

The sum of the coefficients is given by

nC0 + nC1 + nC2 + ... + nCy^(n-1) + y^n

We can use Pascal's identity to simplify this expression:

nC0 + nC1 + nC2 + ... + nCy^(n-1) + y^n = (nC0 + y^n) + (nC1 + y^(n-1)) + ... + (nCn-1)

Pascal's identity tells us that nC0 + y^n = 2^n, so the sum of the coefficients is

2^n + (nC1 + y^(n-1)) + ... + (nCn-1)

This expression is always equal to 2^n. Therefore, the sum of the coefficients of the expansion of (x+y)^n is always 2^n.

In the case of (5a/3-2b/3)^10, x = 5a/3 and y = -2b/3, so the sum of the coefficients is 2^10 = 1024.

GuestJul 14, 2023

+2427

Our badminton team has finished 75% of its season. So far, we have won 20% of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

You've played 75% of the season. So, you've played

75% of the total number of games in the whole season.

You have won 20% of 75% of the total number of games

in the season. That means you've won 15% of the total

number of games in the season.

To achieve that 50% winning season, you will need to win

another 35% of the total number of games in the season.

However, since there's only 25% of the season left, then

there are only 25% of the total number of games in the

season left to play. There aren't enough games left.

You can't achieve a 50% winning season this year.

BoscoJul 14, 2023

This is so true. The website is going down.

GuestJul 14, 2023

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