All Answers 358083 Answers

(Seems like no one want to answer the question after half a day then)

Your entry:P(x)=(x-a)(x-10)(x-20). Given that P(7)=15, what is the value of a?

Lets expand the polynomial P(x) first:

\(P(x)=\left(x-a\right)\left(x-10\right)\left(x-20\right)+15\)

\(=\left(x-a\right)\left(x^2-30x+200\right)\)

\(P(7)=15\)

Plug x=7 into P(x)

\(P(7)=(7-a)(7^2-30\cdot 7+200)=15\)

\(=(7-a)(49-210+200)\)

\(=39(7-a)\)

\(=273-39a\)

We know that \(273-39a=15\)

\(a=-(15-273)/39\)

\(a=-288/39=-96/13\)

14358(1+4%) to the power of 1 over 12 is:

\(\left(14358\left(1+0.04\right)\right)^{\frac{1}{12}}\)

Answer \(≈2.22763\)

The equation for the exchange from celsius to fahrenheit is as follows:

\(F=\frac{9}{5}C+32\)

For your question, plug C=37 in the equation, therefore the answer you are looking for is:

\(F=\frac{9}{5}37+32=98.2\) (Fahrenheit)

404 1264527216 7198410512 0106983499 7342915147 7172148045 5653591241 5553571351 4194979508 0744945211 5938068161 6183246902 3796413516 8783375590 8940065508 0442734197 (153 digits) = 11 × 109^2 × 972119 × 45 8794766603 × 172 9725211873 × 1262 5403074419 6009147841 × 31747 6324118287 6692543363 8881510887 3639133034 5815181089 6280330376 5669567233 0437942957 0985533267 (95 digits)

As you can see, it can factor a good portion of it, but it is STUCK in the last 95 digits!!. This last 95-digit number is not prime but composite, but it cannot handle it so far. It may take it days or weeks to factor it!.

A problem, such as this, requires a multi-step solution.
First, find the FV of $1 per period for the first 5 years @ 5% using this common formula: FV =$1 x (1.05^5 - 1) / 0.05=$5.53. Then project this amount forward for the second 5-year period using this second common FV formula: FV = PV x 1.05^5 =$5.53 x 1.2762815625=$7.05. Then continue this process for eight 5-year periods. You should get the following amounts:
At the end of the first 5-year period =$5.53
At the end of the second 5-year period=$7.05
At the end of the third 5-year period =$14.53
At the end of the fourth 5-year period=$18.54
At the end of the fifth 5-year period =$29.19
At the end of the sixth 5-year period=$37.25
At the end of the seventh 5-year period=$53.07
At the end of the eighth 5-year period =$67.73
This last amount shown to 10 decimal places=$67.7308673760.
Since the young couple's wish is to have $500,000 at 65, then we just divide: $500,000 / $67.7308673760 =$7,382.16 - which is their expected annual payment into their retirement fund. 

a.  As long as a is not -1/2 then there will always be a term in x⁴, so fourth order is the largest possible.

b.  If you choose b = -1/2 then the x⁴ and x² terms vanish and you are left with a linear expression (I.e. first order).

Why must you only use simple functions?

Thanks Chris,

I guess it was the the restriction on z scores that were wanted.   :/

Perhaps next time someone should clarify the rules for the new users, or atleast inform them after passing them. I dont think users should be able to delete their questions like that. However, i think it is understandable if a new user, for whatever reason, passes this rule. I hope miranda will not pass this rule again.

So how well would your algorithm be at breaking down this number?  just curios, for some encrytion im trying

404126452721671984105120106983499734291514771721480455653591241555357135141949795080744945211593806816161832469023796413516878337559089400655080442734197 (153)

Fully expand (x^4+x^3+x^2+x+1)^4

Use this calculator web2.0calc:

The sum of the angles in a quadrilateral  =  360°     So.....

x   +   5x + 15   +   3x - 25   +   4x - 20     =  360

                                                                                 Combine like terms.

13x - 30  =  360

                                                     Add  30  to both sides of the equation.

13x  =  390

                                                     Divide both sides of the equation by  13  .

x  =  30

Since  x  is positive, the largest angle must be  5x + 15 .

( It has the largest coefficient of  x  and all the others either add nothing or subtract something. )

And..... if  x  =  30,       5x + 15  =  5(30) + 15  =  165°

Of course, we talked to her. We take our jobs very seriously.

Here’s a transcript of our conversation.

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After lining up and indexing the inline citations and footnotes of the conversation and cross-referencing those to advanced texts on diagnostic clinical psychology, basic analyses indicated she’s in an existential crisis.

A review by a dozen psychiatrists and behavioral therapists returned a consensus that she’s using deconstructivism motivated by nihilism to define her existential crisis. The suggested treatment plans included electroshock therapy, powerful antipsychotic drugs, and euthanasia.  One outlier suggested banishment. (Humph –there is one in every crowd.)

Admin, who is the final authority, took the advice of the outlier.  Go figure.

Thank you for your concern.  Have a nice day. 

.

Is this your question?

\(\sqrt{l(l-5)}=6\)

                                                   Square both sides of the equation.

\(\sqrt{l(l-5)}^2=6^2 \\~\\ l(l-5)=36\)

                                                   Distribute the  l  to both terms in parenthesees.

\(l^2-5l=36\)

                                                   Subtract  36  from both sides of the equation.

\(l^2-5l-36=0\)

                                                   Use the quadratic formula to solve for  l  .

\(l=\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-36)}}{2(1)} \\~\\ l=\frac{5\pm\sqrt{25+144}}{2} \\~\\ l=\frac{5\pm13}{2} \\~\\ \begin{array} \ l=\frac{5+13}{2}\qquad &\text{or}&\qquad l=\frac{5-13}{2}\\~\\ l=9&\text{or}&\qquad l=-4 \end{array}\)

There are 2 possible interpretations from the statement above. It is either one of the following

1. \((\frac{1000}{2})^{75}\)

2. \(\frac{1000}{2^{75}}\)

I will evaluate both for you, anyway. I have left both answers in plaintext form, so you can copy and paste the answers.:
 

1. \((\frac{1000}{2})^{75}=500^{75}=\)26469779601696885595885078146238811314105987548828125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

2. \(\frac{1000}{2^{75}}=\frac{1000}{37778931862957161709568}\div\frac{8}{8}=\frac{125}{4722366482869645213696}=\)

0.000000000000000000026469779601696885595885078146238811314105987548828125

2.3 million  is  what percent of 325,602,223

2,300,000  =  (what) / 100    *  325,602,223

                                                                             Divide both sides by  325,602,223

2,300,000 / 325,602,223      =  (what) / 100

                                                                             Multiply both sides by  100  .

230,000,000 / 325,602,223  =  what

0.706  ≈  what

So...

Approx. 0.706  percent  of  325,602,223  is  2.3 million .

y=300+.4y

y = 300 + 4y   [ both sides: - 4y

- 3y = 300       [ both sides: div -3

y = - 100

  !

This was asked and answered here:

https://web2.0calc.com/questions/find-t-if-the-expansion-of-the-product-of-x-3-4x#r1

I would argue that there is a second solution to this problem, however. Let me demonstrate why:
 

Now, let's solve each equation separately:

You will notice that the user above also got this answer of a=5. What about the second solution? Well, you'll see. Solve for a in the following equation \(x+a=-\sqrt{x^2+10x+25}\), the second case:

Is this actually a solution, though? If you are ever unsure of whether or not a solution is truly a solution, plug it into the original equation:

Therefore, there are two solutions

\(a_1=5\)

\(a_2=-2x-5\)

It is very difficult with very big numbers. Of course, as long as it is EVEN, you can always divide by 2 until you get an ODD number. After that, it becomes much more difficult. Only very advanced and complicated algorithms can factor such large numbers. Even then, if the number becomes too large, such as 500-digit number, even the fastest supercomputers cannot factor it. And that is how the internet uses huge numbers to encrypt information about online purchases and online banking...etc.

I have such an algorithm on my computer which can crack relatively large numbers, such as this one you came up with:

4917863 8447116951 8665158572 0574258757 9865087301 5832296036 7101810290 0695896488 (77 digits) = 2^3 × 7 × 94 3365688047 3820919255 6236008691 (32 digits) × 930 9115048350 5505083439 9070994494 3748867153 (43 digits)

Ok, so im trying to grasp the math on factoring such a large number

Can you help me out?    Making an even number i think

49178638447116951866515857205742587579865087301583229603671018102900695896488

so i break it down to here

24589319223558475933257928602871293789932543650791614801835509051450347948244

24589319223558475933257928602871293789932543650791614801835509051450347948244

thank you

x^16 + 4 x^15 + 10 x^14 + 20 x^13 + 35 x^12 + 52 x^11 + 68 x^10 + 80 x^9 + 85 x^8 + 80 x^7 + 68 x^6 + 52 x^5 + 35 x^4 + 20 x^3 + 10 x^2 + 4 x + 1 .
 
See Melody's answer to this question to learn how to calculate the coefficients:
http://web2.0calc.com/questions/what-is-the-coefficient-of-a-4b-2-in-the-expansion

Well, you could divide your number by any smaller number such as 2 and adjust the last digits to add up to your original number. So dividing by 2 will give you these 2 numbers. The number is not EVEN, so you get a fraction at the end because you are dividing 7 by 2 =3.5. Then adjust the last 2 digits to 3 and 4 and then add the 2 numbers together to get your original number. Like this:

35702972027818625020095973668955176075524075656581999407158027131028227791043 + 35702972027818625020095973668955176075524075656581999407158027131028227791044=

71405944055637250040191947337910352151049351313163998814316054262056455582087.

You could do that by dividing it by any number from 2 and up. You could also subtract any number you want from your original number and have two numbers that will add up to your original number. However, it is much more difficult to factor such large number into its prime factors. This one turns out to be relatively easy to factor. This is much more important in math than just finding two numbers that will add up to the original number:

7140594 4055637250 0401919473 3791035215 1049351313 1639988143 1605426205 6455582087 (77 digits) = 11 × 1092 × 972119 × 172 9725211873 × 3249 3174077067 1429652325 3645629856 3167127445 2972086011 (54 digits).

Have fun with numbers!!.

if (x+a)^2=x^2+10x+25 what is the value of a?

\((x+a)^2=x^2+10x+25\\ (x+{\color{blue}a})^2=(x+\color{blue}5)^2\\ \color{blue}a=5\)

  !