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stealth61 [152]
3 years ago
10

Determine whether y varies directly with x. Find the constant of variation. Write the function rule x 5 7 9 y 6 11 16

Mathematics
1 answer:
daser333 [38]3 years ago
4 0

Answer:

  a)  y does NOT vary directly with x

  b)  y = 2.5x -6.5

Step-by-step explanation:

If variation were direct the ratios of y to x would be constant. They are not:

  6/5 ≠ 11/7

y does not vary directly with x.

__

y changes by 5 from 6 to 11 when x changes by 2 from 5 to 7. Then the slope of the linear function rule is (change in y)/(change in x) = 5/2. Using a point-slope form of the equation of a line, we can write the rule as ...

  y = m(x -h) +k . . . . . . . . for a line of slope m through point (h, k)

  y = (5/2)(x -5) +6

  y = 2.5x -6.5 . . . . . simplify

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From the table, we have the following values

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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the
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Answer:

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Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

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z = 8000/xy

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S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

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8000 = 20(20)z

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z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

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