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If he ate 1/3 of the pie and 8 pieces are left then 8 pieces = 2/3 of the pie and that means 4 pieces = 1/3 of the pie meaning 12 pieces = 3/3 of the pie so the pie was originally cut into 12 pieces.

when we are finding Z we can use the information in the question \(z^3+14=-74+ci\) and we find out that \(z = \sqrt[3]{ci-88}\)

Base 3 largest 4 digit number   2222  =  80₁₀

  smallest   base 3 number        1000 =  27₁₀

Largest 2-digit base 6      55  =  35₁₀

  smallest                          10  = 6₁₀

So  the numbers that are 4 digit in base 3   and 2 digit in base 6 go from 27₁₀  thru  35₁₀        I'll let you finsish from here......

We know that there are 8 items in 1 set and he sold 112 items so... our equation is 112/8 = 14 and we know each set sold 2 pens so... 14*2 = 28 pens sold altogether.

You are welcome !

a)  substitute  t = 10 into the equation to find their height at ten seconds

        subtract this height from 5500  to find how far they have falllen

b) sbstitute 1000 for  H    then solve for  t   in the equation

c)  h will = 0 when they smack into the ground if they do not open a chute

           use H = 0     to find the total time to fall from the plane to the ground

               then subtract the answer from b to find how much time is left !

thank you!

When they meet, they have covered one full lap of the track together

  they meet at 30 seconds, then

  alice takes 20 more seconds  for a total of 50 seconds per lap

  alice has covered 3/5    and  bert has only covered 2/5  of a lap

2/5 x = 30 seconds

x = 75 sec for bert -lap

(-3-4)/(-4-y) = 1/7

7(-3-4) = (-4-y)

-21-28 = -4-y

21+28 = 4+y

49 = 4+y

45 = y

I hope this helped. :))

=^._.^=

Here is one way   start at 99 and count backwards by 5's until you hit a multiple of 12

   99 - 5 = 94

         94 - 5 = 89

             89 - 5 = 84    Bingo !     84/12 = 7 large boxes     and 3 small boxes

But wait....     what about 24 ?     then there would be 2 large boxes    and  15 small boxes

Find per unit wt of tack

(1590 - 1470) / 40    gm / tack

Now divide starting wt / unit weight to find tacks

1590 gm /  [(1590 - 1470) / 40] gm/tack     = 530 tacks

You can see from the diagram that Henry is 24 ft   east and   32 ft south of his start

   using pythag theorem

      24^2 + 32 ^2 = d ^2

           d = 40 ft from the starting point

First , find out how much money they had to start

a       +      a-48       = 160

2a = 208

a = 104       then t =  56

the t spends some money and this is the result:

(56 - s) *4   =  104

224 - 4s = 104

-4s = -120

s = 30                       t   spent   $ 30 at the store  

Godamn

Hey there, Guest!

So the perimeter of a circle is also called the circumference.

\(C=2\pi r\)

\(2\pi 3\)

\(6\pi \)

\(6\pi/2\)\(=\) 3pi cm

And there's your answer.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Hey there, Guest!

I have created your graph here: https://www.desmos.com/calculator/hmtatkdegq

Hope this helped! :)

( ﾟдﾟ)つ Bye

If, f(x)=sin(x/2), then there exists a number c in the interval  pi/2 < x < 3pi/2  that satisfies the conclusion of the Mean Value Theorem. What is the value of c ?

Hello Guest!

\(f(x)=sin(\frac{x}{2})\\ f(\frac{\pi}{2})=sin(\frac{\pi}{4})=\frac{1}{2}\sqrt{2}\\ f(\frac{3\pi}{2})=sin(\frac{3\pi}{4})=\frac{1}{2}\sqrt{2}\)

The secant through these function values has a slope of 0, , like the tangent in the maximum of the function.

\(f(x)=sin(\frac{x}{2})\\ \frac{df(x)}{dx}=\frac{1}{2}cos(\frac{x}{2})=0\\ \color{blue}x_{max}=\pi\)

\(f(x)=sin(\frac{x}{2})\\ \color{blue}f_{max}(x)=f(\pi)=sin(\frac{\pi}{2})=1\)

\(\color{blue}The\ value\ of\ c\ is\ (\pi,1).\)

  !

The mean value theorem here says:

Can you finish from here?

Since area is \(A=\pi r^2\)  then  \(\frac{dA}{dt} = 2\pi r\frac{dr}{dt}\)

So the rate of change of area is \(2\pi r\) times the rate of change of radius.

I'll leave you to plug in the numbers.

Arc ED = 32º

Arc EA = 148º

Arc BDC = 148º

Wanda and Louise determine that the expression A =-2w^2+36w models the area of a rectangular puppy run, where w is the width in metres and A is the area in square metres. What dimensions produce an area of 112 m2

Hello Guest!

\( A =-2w^2+36w \\ -2w^2+36w -A=0\\ -2w^2+36w -112=0\\ w^2-18w+56=0\)

\(w=-\frac{p}{2}\pm \sqrt{(\frac{p}{2})^2-q}\\ w=9\pm \sqrt{9^2-56}\\ w=9\pm 5\\ \color{blue}w_1=4m\\ \color{blue}l_2=14m\)

\(l_1=A/w_1=112m^2/4m\\ \color{blue}l_1=28m\\ w_2=A/l_2=112m^2/14m\\ \color{blue}w_2=8m\\\)

The dimensions \({\color{blue}4m\times 28m}\ and\ \color{blue}8m\times 14m\) produce an area of \(\color{blue}112 m^2.\)

  ! 

x² +10x + 25 = 8

x² +10x +17 = 0

x = -5 +2√2      or      x = -5 -2√2