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Mariulka [41]
3 years ago
6

Find an equation of variation for the given situation: y varies jointly as x and the square of z and inversely as w, and y= 27/

2 when x =2, z=3, and w=8.

Mathematics
1 answer:
Elodia [21]3 years ago
7 0

9514 1404 393

Answer:

  y=\dfrac{6xz^2}{w}

Step-by-step explanation:

When y varies jointly as x and z, the equation is written ...

  y = k·x·z

Here, the joint variation is not with z, but with z². There is also an inverse variation with w, so the entire relation is ...

  y = k·x·z²/w

We want to find the value of k for the given values of the variables. So, we can solve for k to get ...

  k=\dfrac{wy}{xz^2}=\dfrac{8\cdot\dfrac{27}{2}}{2\cdot3^2}=\dfrac{4\cdot27}{2\cdot9}=2\cdot3=6

Then the equation of variation is ...

  \boxed{y=\dfrac{6xz^2}{w}}\qquad\textbf{matches B}

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How do you simplify this and write as a polynomial in standar form? (x-9)3x-7)+(3x^2-5x+2)​
nasty-shy [4]

Answer:

Standard form of (x-9)(3x-7) + (3x^{2} - 5x+2) =6x^{2}  - 39x + 65

Step-by-step explanation:

Here, the given expression is (x-9)(3x-7) + (3x^{2} - 5x+2)

Now, simplifying the above expression in parts, we get

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hence, combining both parts:

(x-9)(3x-7) + (3x^{2} - 5x+2)=(3x^{2}   -34x +63) + (3x^{2} - 5x+2)

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The above expression is of the STANDARD FORM: ax^{2}  +bx + c

Hence, the standard form of (x-9)(3x-7) + (3x^{2} - 5x+2) =6x^{2}  - 39x + 65

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