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Find the constant term in the expansion of \(\left(2z - \frac{1}{\sqrt{z}}\right)^9\).

\(\begin{array}{|rcll|} \hline && \dbinom{9}{6}*(2z)^3*\left(\frac{1}{\sqrt{z}}\right)^6 \\\\ &=& \dbinom{9}{6}*8z^3*\dfrac{1}{z^3} \\\\ &=& \dbinom{9}{6}*8\\\\ &=& \dbinom{9}{9-6}*8\\\\ &=& \dbinom{9}{3}*8\\\\ &=& \dfrac{9}{3}*\dfrac{8}{2}*\dfrac{7}{1}*8\\\\ &=& 3*4*7*8 \\\\ &=& 672 \\ \hline \end{array}\)

I'd say it's pretty self-explanatory, cuz from unit conversion we get 1g/cm^3 =  1000kg/m^3

From the 9th term to the 25th term is 16 common differences

    -6   + 16 d   = 25th term

     -6   + 16 ( 5/4) =   14

How?

WolframAlpha says it is 84     ....but I do not know how to derive it ....Anyone?

Area of triangular pyramid is   1/3 * base area * height

   can you find the area of an equilateral triangle with sides = 14 ?

y = k/x^2

yx^2 = k

15 (24)^2 = 8640

13 (x^2) = 8640

x^2 = 8640 / 13

x = 25.78          (taking the positive root)

 3(x - 4) + 2(x^2 - x + 7) - 5(x - 1) + 8(x^2 - x + 3) - 4(x - 5)

3 (-4)     +  2(7)             -5(-1)       ......                                      can you finish ?

Find the range of the function f(x) = 9^x - 3^x + 1.

Hello Guest!

The range is the space between the minimum of the function and the maximum value.

\( f(x) = 9^x - 3^x + 1\\ \frac{df(x)}{dx}=9^xln\ 9-3^xln\ 3=0\\ 9^xln\ 9=3^xln\ 3\)

\(x_{min}= -0.6309297535714576\)

\(f(x) = 9^x - 3^x + 1\\ f(x_{min}) = 9^{(-0.6309297535714576)} - 3^{(-0.6309297535714576)} + 1\)

\(f(x_{min})=0.75\)

\(\color{black}The\ range\ is\\ f(x)\in \mathbb R\ |\ 0.75\leq y<\infty\)

  !

thank you melody!!!

anyone??

cant, sorry :(

SOMEONE PLS HELP

Daniel is traveling 5 m/hr faster and will take   1/3 m / 5 m/hr   to close the 1/3 mile gap =  1/15 hr = 4 minutes

Anyone who owns a cat  is totalled with anyone who owns a dog       16 + 11 - 7 =  _______   people own a cat or dog.

Hi Guest,

Systems of Equation w/ Quadratics 

x - y = 12

y^2 = 5(x-2)

x = y + 12

y^2 = 5(y + 12 - 2)

y^2 = 5(y + 10)

y^2 = 5y + 50

Forms a quadratic: y^2 - 5y -50 = 0

Factor:

(y + 5)(y-10)

y = -5, y=10

So x = 7, x = 22

it says thats wrong sry

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The shaded area is everything ABOVE and INCLUDING the line...

Calculate the equation of the line to be   y = - x + 1

    so the shaded area      y >= -x+1

c = 6      v = 22       

h = - 16t^2 + 22t + 6

10 = - 16t^2 + 22t  + 6

-16t^2 + 22t -4 = 0       Use quadratic formula to find t = .215    and     1.15     sec    

                                          so yes, it will reach 10 ft as we have times for it on the way up and down

By the Biniomial Theorem, the constant term is C(9,5)*2^4 = 2016.

Hi justinwh333,

Question has already been answered: https://web2.0calc.com/questions/please-help_20319#r2

Hi justinwh333,

Your question is already answered here: https://web2.0calc.com/questions/please-help_20319#r2 

x - y = 12

y = x - 12

y^2 = 5(x - 2)

(x-12)^2 = 5(x - 2)

=^._.^=

Hi Guest,

Factor out the 4 in 4x^2 + 15x + 2

You should have: 

4(x^2 + 15x/4 + 1/2)

Next, add and subtract (15/8)^2

4(x^2+15x/4 + 1/2 + (15/8)^2 - (15/8)^2)

Finally, complete the square:

4((x + 15/8)^2) + 1/2 - (15/8)^2)

Answer is: 4(x + 15/8)^2 - 193/16

A = 4, U = 15/8, V = -193/16