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1 year ago

If x=z+8 where z varies inversely as y and z=2 when y=3 find relation between y and x?

Mathematics

1 answer:

sattari [20]1 year ago

5 0

Answer:

y = 6/(x - 8).

Step-by-step explanation:

z = k/y where k is a constant

2 = k/3

k = 6.

So z = 6/y

and x = 6/y + 8

Multiply through by y:

xy = 6 + 8y

xy - 8y = 6

y(x - 8) = 6

y = 6/(x - 8)

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Given the polynomial expression:

(y + 5)²

(y - 5)(y + 5)

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a.) (y + 5)²

The given equation is a factor of a perfect square trinomial. For this type of expression, the following is the formula for expanding it.

$\text{ (a+b)}^2\text{ = }a^2\text{ + 2ab + }b^2$

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b.) (y - 5)(y + 5)

To be able to simplify the following expression. We will be using the formula for the difference of two squares.

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We get,

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$x^{2} -12x=13\ \ \ \Leftrightarrow\ \ \ x^2-2\cdot x\cdot 6+6^2-6^2=13\\\\ \Leftrightarrow\ \ \ (x-6)^2=13+36\ \ \ \Leftrightarrow\ \ \ (x-6)^2=49\ \ \ \Leftrightarrow\ \ \ (x-6)^2=7^2\\\\x-6=7\ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ x-6=-7\\\\x=13\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-1\\\\Ans.\ x\in \{-1,\ 13\}$

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2 years ago

Read 2 more answers

If x=z+8 where z varies inversely as y and z=2 when y=3 find relation between y and x?​

If x=z+8 where z varies inversely as y and z=2 when y=3 find relation between y and x?