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Perhaps you are unfamiliar with the floor function asinus.

\(f(x) = x - \lfloor \sqrt{x} \rfloor^2\\ f(101)=101-\lfloor \sqrt{101} \rfloor^2=101-10^2=101-100=1 \\ f(102)=102-100=2\\ f(103)=3\\ ...\\ f(110)=10\\ \)

So the sum is 1+2+3+...+10 = 1+10+2+9+3+8+4+7+5+6 = 11*5 = 55

I have not checked my answer carefully.

D= daught age now.     10 years ago.    D-10.     And mother was M-10= 7 (D-10)

NOW.     M= 2D.      Sub this into the fjest equation

2D - 10 = 7D-70

60=5D.      D = 12.    

 Then M = 2D= 24.   ( Mom was preggo @ 11 y/o ! )

1)  EF || GH   --->   arc(EH) = arc(FG)   --->   x² - 2x  =  56 - 3x

                                                                  x² + x - 56  =  0

                                                               (x + 8)(x - 7)  =  0

                                                                                 x  =  7                      (can't be negative)

    I don't know how to use this value for x to find arc(EPF) because I don't know where P is.

2)  Because this is a regular dodecagon, each side is congruent to every other side.

     Since you haven't had any trig, try this:

     Within the regular dodecagon,

     --  Draw the regular hexagon  P₁P₃P₅P₇P₉P₁₁  (with the center of the circle = O)

          Since it is a regular hexagon, angle(P₁OP₃)  =  60^o      

          OP₁  =  OP₃ =  P₁P₃  =  1

     --  Draw the diameter of the circle that goes through P₂.

          This bisects angle(P₁OP₃) and also bisects P₁P₃  --  call this point X.

    --  P₁X · XP₃  =  P₂X · XP₈        (P₈ is the other end of the diameter from P₂)

         P₁X  =  XP₃  =  1/2

         Let P₂X  =  x   --->   XP₈  =  2 - x

         P₁X · XP₃  =  P₂X · XP₈   --->   (1/2)(1/2)  =  (x)(2 - x)

                                                                     1/4  =  2x - x²

                                                        x² - 2x - 1/4  =  0

          By the quadratic formula:  x  =  ( 2 - sqrt(3) ) / 2

       Now, look at triangle P₁XP₂  --  it is a right triangle with P₁P₂ the hypotenuse

       Using the Pythagorean Theorem:  (P₁P₂)²  =  (1/2)² + ( 2 - sqrt(3) )²   

                    --->   P₁P₂  =  2 - sqrt(3)

To find your answer, you'll need to square this and multiply by 12.

The RDA  is the recommended daily allowance of the vitamin.      If you get more than this amount it is more than 100% of the RDA....

The angle that has tan = a/b. (Remember tan= opp/adj)    Is the angle at the lower right....cos of this angle would be adj/ hyp =b/ ((sqrta²+b²))

40% of 25000  =  0.40 x 25000  =  10000

30% of 10000  =  0.30 x 10000  =  3000

20% of 3000  =  0.20 x 3000  =  600

10% of 600  =  0.10 x 600  =  60

More simply, just do this:  0.10 x 0.20 x 0.30 x 0.40 x 25000  =  60

Generally speaking, you can't turn an  x - 1  into an  x + 1.

You can turn a  1 - x  into an  x - 1  by factoring out a negative one:  1 - x  =  -1(x - 1)

  x = 2.5    --->    2

2x = 5.0    --->    5

3x = 7.5    --->    7

\(f(x) = x - \lfloor \sqrt{x} \rfloor^2\\ f(101) = 101 - \lfloor \sqrt{101} \rfloor^2=0\\ f(102) = 102 - \lfloor \sqrt{102} \rfloor^2=0\\ What\ is\ wrong?\\ Greetings \)

  !

Let  3x  be the number of girls 

and 2x  be the number of boys.

Seven more girls join the class:  the number of girls is now  3x + 7

Two boys drop the class:            the number of boys is now  2x - 2.

The ratio of girls to boys is now 5:2     --->     (3x + 7) : (2x - 2)  =  5 : 2

         (3x + 7) / (2x - 2)  =  5 / 2

                  2 · (3x + 7)  =  5 · (2x - 2)

                         6x + 14  =  10x - 10

                                 24  =  4x

                                   6  =  x

Current number of girls:  3x + 7   --->   3(6) + 7  =  25

Current number of boys:  2x - 2   --->   2(6) - 2  =  10

Ronald is a baseball player.  When he hits a baseball, the height of the ball can be modeled by the following function, where t is the number of seconds after the ball is hit and h(t) is the height of the ball in feet after t seconds.

h(t)=−16t2+90t+4

a)  What is the maximum height that the ball reaches?

b)  How long does it take for the ball to reach its maximum height?

c) How long does it take for the ball to hit the ground?

Round all answers to the nearest tenth of a foot or second.

Ronald ist ein Baseballspieler. Wenn er einen Baseball schlägt, kann die Höhe des Balls durch die folgende Funktion modelliert werden, wobei t die Anzahl der Sekunden nach dem Schlagen des Balls und h (t) die Höhe des Balls in Fuß nach t Sekunden ist.
a) Was ist die maximale Höhe, die der Ball erreicht?
b) Wie lange dauert es, bis der Ball seine maximale Höhe erreicht hat?
c) Wie lange dauert es, bis der Ball den Boden berührt?

Hello Guest!

\(h (t) = - 16t^2 + 90t + 4\)

b)

\(h'(t)=-32t+90=0\\ t=2.8125\)

\(2.8\ second\ does\ it\ take\ for\ the\ ball\ to\ reach\ ist\ maximum\ height.\)

a)

\(h (t) = - 16t^2 + 90t + 4\\ h (t) = - 16\cdot (2.8125)^2 + 90(2.8125) + 4\\ h(t)=130.5625\\ \color{blue}130.6\ foot\ is\ the\ maximum\ height\ that\ the\ ball\ reaches.\)

c)

\(h (t) = - 16t^2 + 90t + 4=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x = {-90 \pm \sqrt{90^2-4\cdot (-16)\cdot 4} \over 2\cdot (-16)}\\ x=\frac{-90\pm \sqrt{8356}}{-32}\\ x=5.669\)

\(5.7 \ second\ long\ does\ it\ take\ for\ the\ ball\ to\ hit\ the\ ground.\)

  !

Wow he changed his question. MBMT please find this cheater

Wow very clever changing the question so that people won't flame you for cheating on MBMT. I see I see

It is not going to be 0 because the floor of sqrtx is usually smaller than the sqrtx.

Have you tried to work this out yourself guest?

Show us what you have tried.

Hint: there is only 10 functions there. Just do them one by one.  Easy Peazy.   (I expect)

wdym oh god

Drawing it out would help, but I'm new to the "write code to make funny pictures on web2.0.calc" thing so this is the best I can do.

The side of the triangle is ABC = 3a
The side of the hexagon = a
Area of triangle = (root3 /4 )*(3a)^2 = 9a^2 *(root3/4)
Area of hexagon with side a = 6*(root3 /4 )*(a)^2
Ratio of areas of hexagon to that of triangle = { 6*(root3 /4 )*(a)^2 } / { 9a^2 *(root3/4)} = 6/9 = 2/3
and we get = 2 : 3

Yay!

i tried that but that was incorrect

One man can finish in X days.
2 machines finish in 13 days, so 1 machine finishes in 26
3 men and 8 machines finish in 1/2 the time it takes 3 machines and 8 men.
Because of that 3/M + 8/26 = 2(8/M + 3/26)
3/M + 4/13 = 16/M + 3/26
16/M – 3/M = 4/13 – 3/13
13/M = 1/13
M = 169
Number of men to finish the job is: 13 days = 169/13 = 13

Yay!

Let  \(f(x) = x - \lfloor \sqrt{x} \rfloor^2 \) What is \(f(101) + f(102) + f(103) + \cdots + f(110)? \)

Hello Guest!

\(f(x) = x - \lfloor \sqrt{x} \rfloor^2 \)

\(f(101) + f(102) + f(103) + \cdots + f(110)=0 \)

  !

I have just realized that Max has been answering most of your questions.

Now he knows you are an ungrateful m***n  he may not answer any more.  

I can do this. Although it has been a couple years since I studied mesopotamia.

Zoroaster started Zoroastrinism and was an iranian prophet.

Hammurabi wrote hammurabi's code, based off of eye for an eye. His punishments were harsh, but not as harsh as some of the others. It is said that his code actually influenced the US's law system. (But thats what I heard, it might be wrong.)

Nebuchadnezzar (who's name is too long and I'm going to call Chad) was a Babylonian king, who reined for wayyyy too long. He didn't do too much lol.

Sargon was the first Akkadian ruler and conquered the sumerians with his chariots. He was the first ruler of an Empire.

Cyrus the Great created the Archaemenid Empire, later becoming Persia.

Thanks for the recap of Mesopotamia

Yay!

Starting with:  e^i·x  =  cos(x) + i·sin(x)

If  x  =  pi/2   --->   e^i·(pi/2)  =  cos( pi/2 ) + i·sin( pi/2 )

                    --->   e^i·(pi/2)  =  0 + i·1  =  i     --->     i  =   e^i·(pi/2) 

So:  iⁱ  =  ( e^i·(pi/2) )ⁱ  =  e^{i^2 · pi/2}  =  e^-1·pi/2  =  e^{- pi/2}  

mharrigan,

Do not be rude to our values answerers or you there will be consequences.

Do not ask twice.

We are not here to spoon-feed your homework to you but if you do not understand an answer then ask on the original thread.

Hi Dm,

8^1/3   is best expressed as 8^(1/3)               

8^(1/3) =    \(\displaystyle 8^{\frac{1}{3}}=8^{1/3} = \sqrt[3]{8}=2\)

You need the brackets because otherwise 8^1/3 really means   \((8^1) /3  = 8/3 = 2\frac{2}{3} \)