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Thanks though I already solved it...

Now all the questions will be answered independently

Note if works is done independently then permatutions are added. For example if. You need to find make a team of 12 from a class which search two section each Class Section has 12 student the teams who comprise of 6 different from each section then the permutation of 1 section will be added to second sectionto get the total permutations of number of ways in which a team of 12 can be selected

But if. Doing one work depend or influence other then permatutions are multiplied

Ex the combination of four letter word is 4× 3×2×1

So ways in which one question can be answered is. 4! = 24

There are ten question which has to be answered independently so

Total no. Of ways = 10 × 24 = 240

The question was easy but u need to understand when to apply 10! × 4!

And when to apply 10 × 4!

I had explained it above in detail

Hope u get it comment if u want to understand it more briefly but I guess u can understand from this content if u don't comment down and I will repeat the explanatio

https://web2.0calc.com/questions/help-is-appreciated_15

This is very easy...

We have $f(3) = 12(3)^9 + 3$ and $f(-3) = 12(-3)^9 + (-3)$. Adding, this is $12(3)^9 + 3 + 12(-3)^9 + (-3)$. Since $(-1)^9 = -1$, this simplifies as $12(3)^9 + 3 - 12(3)^9 - 3 = \boxed{0}$.

If I understand the notation correctly 460 miles 40^o N of east       then    270 miles 10^o S of east

Find the   components and add them together

460 sin 40 - 270 sin 10    =    248.797  miles North

460 cos 40 + 270 cos 10 =    618.278  miles East

Distance from origin   = sqrt ( 248.797²  + 618.278² ) = 666.46 miles

       angle = arctan ( 248.797/618.278) = 21.92 degrees N of east

Can't see any expressions, but it  should  be something like this  :

Cost   =  [ (800) / y ] *  5.50

Angle at D = x   also     FD is parallel to AC        alternating angles-ish rule

3x + x + 8x = 180 ^o    solve  for x

y intercept will occcur when x = 0

soooo     0 = -y² +2y +3 

               0 = y² -2y-3   factor

                    (y+1)(y-3) = 0                          at y = -1  and  +3        Two y-axis intercepts

Angle C   is also = x   (alternating angles-ish)

angle D = 180 - 50 = 130  

then triangle DBC       130  + x + x = 180      so x = 25 ^o

Hey QM....this is VERY similar to your other question which  I showed you how to answer....you should be able to do this one....try it!

https://web2.0calc.com/questions/help-ep

See final answer posted here:

https://web2.0calc.com/questions/any-help-is-appreciated_5

14 total dishes to choose from

14 * 13  / 2 = 91  different  mix/match plates of two items (if the two item must be different )

sqrt ( q¹²  r¹⁴ )     =     ( q^12 r^14 )^1/2  =   q⁶ r⁷

165 people

s = students                  value = $ 4s   

a = adult tix = 165-s      value = $ 7 (165-s)               summed, the tix =  $ 795

4s            +         7 (165-s)               = 795     

                                                             solve for s

In the initial 20 quarts of mixed paint there is    25% red     sooooo   20 qrts * .25 = 5 quarts of red

now add 4 quarts of red     now there is 9 quarts of red in   20 + 4   quarts

9/24 * 100% = 37.5% red

h = -16t^2 + 48t + 2,        Quadratic equation     a = -16     b = 48    c = 2

                                             max will occur at    t = -b/2a

     use the value of 't' you calculated above    in the equation to calculate the max height.....

The inscribed angle BDC   intercepts the same arc as angle BAC so it is the same measure

    angle B and angle C are equal @ 65^o because of equal side lengths

BAC = 180 - 65 - 65  = BDC

This is the same as saying 'for what values of x is the red line =  -1 '

See graph below....how many points do you see?

h=3+20t-5t^2.       looking for h = 13

13=3+20t-5t^2      re-arrange a bit

-5t² +20t -10 = 0         divide by -5

t² -4t +2 = 0    use Quadratic Formula     

a = 1      b = -4        c = 2

\(t= {-4 \pm \sqrt{(-4)^2-4(1)(2)} \over 2(1)}\)

Hi Dragan! Thanks for your answer! Just wondering, how do you know PQA and CRD are similar? Thanks again! 

The sum of the coordinates is 8 + 27 = 35.

How did you work out 900 divided by 225 = 4^2 ? 

For everyone who is helping me solve this problem, yes, the cross-sections are parallel to the yz-plane.

If one zero of the quadratic is the reciprocal of the other, then their products of the two zeroes must be equal to 1.

By Vieta's, the product of the two zeroes of a polynomial is equal to the constant term divided by the quadratic term. So:

\(\frac{-k}{3}=1\\ -k=3\\\boxed{k=-3}\)

4/3 = 1 1/3

Let the sequence be      a-d,  a,  a+d

So 

\(x^3-6x^2-13x-k=(x-(a-d))\;x\;(x-(a+d))\\ x^3-6x^2-13x-k=x\;((x-a)+d))\;(x-a)-d))\\ x^3-6x^2-13x-k=x\;((x-a)^2-d^2)\\ etc\)

Simplify it down and equaet coefficients.