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tatyana61 [14]
2 years ago
14

Ya idk how to do this plz help explain if you can

Mathematics
1 answer:
Svet_ta [14]2 years ago
5 0

Answer:

  92 attendees had activity cards

Step-by-step explanation:

Let x be the number of students with activity cards. Then 130-x is the number without, and the total revenue is ...

  7x +10(130 -x) = 1024

  7x +1300 -10x = 1024 . . . . eliminate parentheses

  -3x = -276 . . . . . . . . . . . . . collect terms; subtract 1300

  x = 92 . . . . . . divide by 3

92 students with activity cards attended the dance.

_____

<em>Comment on the solution</em>

Often, you will see such a problem solved using two equations. For example, they might be ...

Let 'a' represent the number with an activity card; 'w' the number without. Then ...

  • a+w = 130 . . . . the total number of students
  • 7a +10w = 1024 . . . . the revenue from ticket sales

The problem statement asks for the value of 'a', so you want to eliminate w from these equations. You can do that using substitution. Using the first equation to write an expression for w, you have ...

  w = 130-a

and making the substitution into the second equation gives ...

  7a +10(130 -a) = 1024

This should look a lot like the equation we used above. There, we skipped the extra variable and went straight to the single equation we needed to solve.

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Use the Chain Rule to find the indicated partial derivatives. z = x^4 + xy^3, x = uv^4 + w^3, y = u + ve^w Find : ∂z/∂u , ∂z/∂v
k0ka [10]

I'll use subscript notation for brevity, i.e. \frac{\partial f}{\partial x}=f_x.

By the chain rule,

z_u=z_xx_u+z_yy_u

z_v=z_xx_v+z_yy_v

z_w=z_xx_w+z_yy_w

We have

z=x^4+xy^3\implies\begin{cases}z_x=4x^3+y^3\\z_y=3xy^2\end{cases}

and

\begin{cases}x=uv^4+w^3\\y=u+ve^w\end{cases}\implies\begin{cases}x_u=v^4\\x_v=4uv^3\\x_w=3w^2\\y_u=1\\y_v=e^w\\y_w=ve^w\end{cases}

When u=1,v=1,w=0, we have

\begin{cases}x(1,1,0)=1\\y(1,1,0)=2\end{cases}\implies\begin{cases}z_x(1,2)=12\\z_y(1,2)=12\end{cases}

and the partial derivatives take on values of

\begin{cases}x_u(1,1,0)=1\\x_v(1,1,0)=4\\x_w(1,1,0)=0\\y_u(1,1,0)=1\\y_v(1,1,0)=1\\y_w(1,1,0)=1\end{cases}

So we end up with

\boxed{\begin{cases}z_u(1,1,0)=24\\z_v(1,1,0)=60\\z_w(1,1,0)=12\end{cases}}

3 0
3 years ago
Plz help with math homework
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Where is the question. though
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Write the equation of the line in slope intercept from given the slope of the line is m=3 and the line passes through the point
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Step-by-step explanation:

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ehidna [41]

Answer:

(-2,6) is the codinates of S

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3 years ago
How can you get 3/3 -1/6?
cluponka [151]

9514 1404 393

Answer:

  5/6

Step-by-step explanation:

Addition or subtraction of fractions requires a common denominator. The value 3/3 can be multiplied by 2/2 to give 6/6, which has the same denominator as the other fraction.

  \dfrac{3}{3}-\dfrac{1}{6}=\dfrac{3\cdot2}{3\cdot2}-\dfrac{1}{6}\\\\=\dfrac{6}{6}-\dfrac{1}{6}=\dfrac{6-1}{6}=\boxed{\dfrac{5}{6}}

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