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3 years ago

8/v + 9/x=y Solve for v

Mathematics

1 answer:

Andreas93 [3]3 years ago

4 0

The answer is v= -8x/-xy+9

Here is the step by step process (This is going to be long):

1. 9v+8x=vxy

Multiply both sides by vx

2. 9v+8x+−vxy=vxy+−vxy

−vxy+9v+8x=0

Add -vxy to both sides

3. −vxy+9v+8x+−8x=0+−8x

−vxy+9v=−8x

Add -8x to both sides

4. v(−xy+9)=−8x

Factor out the variable v

5. v(-xy+9)/-xy+9 = -8x/-xy+9

v = -8x/-xy+9

Divide both sides by -xy+9

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Answer:

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Step-by-step explanation:

Given:

The function is given as;

$f(x)=8x^2$

In order to find the inverse, the steps to be followed are:

Step 1: Replace $f(x)$ by $y$ . This gives,

$y=8x^2$

Step 2: Switch 'y' by 'x' and 'x' by 'y'. This gives,

$x=8y^2$

Step 3: Solve for 'y'.

Dividing both sides by 8, we get:

$\frac{x}{8}=\frac{8y^2}{8}$

$\frac{x}{8}=y^2$ or

$y^2=\frac{x}{8}$

Taking square root on both sides, we get:

$\sqrt{y^2}=\sqrt{\frac{x}{8}}$

$y=\frac{1}{2}\sqrt{\frac{x}{2}}$

Now, we replace 'y' by $f^{-1}(x)$ .

Therefore, the inverse of the given function is:

$f^{-1}(x)=\frac{1}{2}\sqrt{\frac{x}{2}}$

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8/v + 9/x=y Solve for v​

8/v + 9/x=y Solve for v