Math  /  Algebra

QuestionSuppose that yy varies inversely with xx, and y=4y=4 when x=6x=6. (a) Write an inverse variation equation that relates xx and yy.
Equation: \square (b) Find yy when x=3x=3. y=y=\square

Studdy Solution

STEP 1

1. y y varies inversely with x x .
2. When x=6 x = 6 , y=4 y = 4 .
3. We need to find the inverse variation equation and calculate y y when x=3 x = 3 .

STEP 2

1. Understand inverse variation.
2. Derive the inverse variation equation.
3. Use the equation to find y y when x=3 x = 3 .

STEP 3

Inverse variation means that y y is proportional to the inverse of x x , which can be expressed as y=kx y = \frac{k}{x} , where k k is a constant.

STEP 4

Using the given values y=4 y = 4 when x=6 x = 6 , substitute into the inverse variation equation:
4=k6 4 = \frac{k}{6}
Solve for k k :
k=4×6=24 k = 4 \times 6 = 24

STEP 5

Now, substitute k=24 k = 24 back into the inverse variation equation:
y=24x y = \frac{24}{x}
This is the inverse variation equation relating x x and y y .
Equation: y=24x y = \frac{24}{x}

STEP 6

To find y y when x=3 x = 3 , substitute x=3 x = 3 into the equation:
y=243 y = \frac{24}{3}
Calculate y y :
y=8 y = 8
The value of y y when x=3 x = 3 is:
y=8 y = 8

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