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(15 +12) / 2   *   6   = ______   cm^2

Since  x = 1  is a vertical asymptote, the expression  x - 1  will be found in the denominator.

Since  x = 2  is a vertical asymptote, the expression  x - 2  will be found in the denominator.

Thus, the function is:  f(x)  =  (x + 4) / ( (x - 1)(x - 2) )

If you multiply out  (x - 1)(x - 2),  you will be able to find the values of a and b.

Can't say without knowing initail velocity .

Example     travelling  10 m/s

 x =     xo + vo t - 1/2 a t^2

            3.3 + 10(2.4) - 1/2 a(2.4^2 )      a (decceleration) = 9.48 m/s^2

Example 2    travelling  20 m/s

               3.3  + 20 (2.4) - 1/2 a(2.4)^2    a = 17.81 m/s^2

Soooo  you need to know the initial velocity to know how fast they slowed down to a stop  ( the deccelaration)

1357 , 1375 , 1537 , 1573 , 1735 , 1753 , 3157 , 3175 , 3517 , 3571 , 3715 , 3751 , 5137 , 5173 , 5317 , 5371 , 5713 , 5731 , 7135 , 7153 , 7315 , 7351 , 7513 , 7531 , Total =  24 such integers

Hi, So we know that there are 360 degrees in a cirle. 40 degrees of the circle has an area of 4pi. We know that 40/360=1/9th of the total circle so we multiply so 1/9 of the are of the circle equals 40pi

 1/9(area of the circle)=4pi

 do some algebra and get that the full circle's area is 36pi units^2.

 The equation for the are of a circle is pir^2

pir^2=36pi

divide both sides by pi

r^2=36

so this could be -6 or 6 but by convention we know that that a radius can be nagative so my answer is 6

Hello Guest,

Can anyone use the p-q formula to solve this equation?

\(x^2+2x=8\)

Thanks in advance

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the p-q formula: \(x_1 \mbox { and } x _2 = -\frac{p}{2} \pm \sqrt{\Big(\frac{p}{2}\Big)^2-q}\) .

\(x^2 + 2x = 8 \ |\ -8\)

. . . let \((p, \mbox { } q) = (2, \mbox { } -8)\) .

\(x_1 \mbox { and } x_2 = \frac{-2}{2} \pm \mbox {} \sqrt{\Big(\frac{2}{2}\Big)^2-(-8)}\)

\(x_1 \mbox { and } x_2 = -1 \pm \mbox {} \sqrt{ 1 + 8 }\)

\(x_1 = -1 + 3\)

\(x _1 = 2\)

\(x_2 = -1 - 3\)

\(x_2 = -4\)

This equation has two solutions, namely \(x_1 = 2\) and \(x_2 = -4\) .

Hope this was helpful. ^^

 !

rational coefficients

Hello Guest!

\(f(x)=(x-1+\sqrt{2} )\times (x-2-\sqrt{7})\\ f(x)=(x^2-2x-x\sqrt{7}-x+2+\sqrt{7}+x\sqrt{2}-2\sqrt{2} -\sqrt{2\cdot 7})\\ f(x)=x^2+(-2-\sqrt{7}-1+\sqrt{2})x+\sqrt{7}-2\sqrt{2} -\sqrt{2\cdot 7} \)

\(f(x)=x^2-4.2315x-5.1559\)

Does the function with rational coefficients exist? I do not think so.

  !

No. of papayas = No. of mangoes = x

He threw 85 papayas

 then remaining papayas = x - 85

 sold = (x-85) * 1/4 -----(1)

He threw 60 rotten mangoes the

  remaining mangoes = (x - 60)

 sold mangoes = (x - 60) 1/3.

Now (No. of Remaining)

        ( Mangoes after    ) = (No.  of Remaining)

        (      selling           )     ( papayas after      )

                                           ( selling                 )

      (x - 85) - (\( {x - 85\over 4}\)) = (x - 60) - (\( {x - 60 \over 3})\)
  => (x - 85) (1 - \({1 \over 4}\)) = (x - 60) (1 - \( {1 \over 3}\))

  => (x - 85) * 3/4 = (x - 60) 2/3

  => 9x - 85 * 9 = 8x - 60 * 8

  =>  x = 85 * 9 - 60 * 8

           = 765 - 480

        x  =  285

  sold mangoes (x - 60) * \( {1 \over 3}\)

                      = (\( {(285 - 60) \over 3} = {225 \over 3} = \)

                      = 75

    3 For $ 5.8

  Collected Money = \( {75 \over 3} * 5.8\)

                             = 25 * 5.8 = 145.0$

                                                    Ans 

Need clarification ... "such that x^2 + xy + y^2"  does what?  

k = 38.

wouldn't there be some value for time uin the equation? You're using d = rt after all

Hello Guest,

Solve for x and y such that \(x^2-y=xy\) . 

There are 2 pairs for (x, y), namely:

\((x, \mbox { } y) = ( 0, \mbox { } 0)\) and

\((x, \mbox { } y) = (-2, \mbox { } -4)\)

Hope this was helpful.

Straight

Hello Guest,

Jeff was on his way to visit his mother in Königshausen.

In doing so, he had to cross the river "Benk" by boat, so he did.

It took 1h and 40 min to cross it with an average speed of 48 km/h. During the trip he said that the river is only 90 km long.

    a) Is his statement true, give reasons.

    After he crossed the river and was finally with his mother, she baked him a cake, saying that it would only take \(\frac{3}{4} \cdot 32\) min.

    After it was ready, she cut it into 3 equal parts. 

    b) Show if this is possible (you may be able to show a picture here).

    c) "I s*ck at math!", Jeff says. 

        Explain to Jeff how to proceed here with the corresponding solution.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    a) His statement is not true, because if we take the remaining 40 min, that corresponds to \(\frac{2}{3}h\) .

        So it took \(48 \mbox { } km + (\frac{2}{3} \cdot 48 \mbox { } km)\) and that is equal to 80 km.

    b) I can show you a picture here:

       I do not think, I must write something here. (The picture is from Google.)

    c) I think that the duration of the baked cake is meant here.

       \(\frac{3}{4} \cdot 32 = \frac{3 \cdot 32}{4} = \frac{96}{4} \mbox { } min = 24 \mbox { } min\) , so it takes 24 min until the cake is ready.

I hope that was helpful. 

Straight

Example: 1 3 7

For the first number, you have 12 choices.

For the 2nd number, you have 10 choices [which excludes the first choice and its consecutive number]

For the 3rd number, you have only 8, choices [excluding the 1st and the 2nd and its consective number]

So, you have: 12  x  10  x  8 ==960 ways of picking 3 numbers out of 12.

n ==1407  2814  4221  5628  7035  8442  9849  Total =  7 [up to 10,000]

The smallest n ==1,407

You have a total of: 4  x  6 ==24 products

Since a prime is only divisible by 1 and itself, it therefore follows that can you only have: 

1  x  5 ==5   and   1  x  7==7

Therefore, the probability is:  2 / 24 ==1 / 12

I am not sure what kind of answer you are looking for

I expanded    \((x+\frac{1}{x})^n\)

and got

\(x^n+\frac{1}{x^n}=k^n-\displaystyle \sum_{r=1}^{n-1}\binom{n}{r} x^{n-2r}\)

1 mL of water weighs 1 gram.   Maybe you are meant to assume the same thing with acetic acid

5.002% of 240 = ?

% means divide by 100 and of means  multiply so you can do that on any calculator

You can expand it out. Replace the 2 with a and the 3 with b

I suppose you could just expand it out but there is probably a better method

\((a^{2^0}+b^{2^0})(a^{2^1}+b^{2^1})(a^{2^2}+b^{2^2})(a^{2^3}+b^{2^3})(a^{2^4}+b^{2^4})(a^{2^5}+b^{2^5})\\\)

According to Wolfram alpha

(40 - x)(64 - x) = 1792

x = 8            (x => the width of the gold cross)

PQ = 36 

I don't know of any solution.