Math

QuestionIf 5x5 x is inversely proportional to y2y^{2} and x=4,y=5x=4, y=5, find yy when x=400x=400.

Studdy Solution

STEP 1

Assumptions1. The relationship between xx and yy is given by 5x=k/y5x = k/y^{}, where kk is a constant of proportionality. . The values of xx and yy at a certain point are given as x=4,y=5x=4, y=5.
3. We need to find the value of yy when x=400x=400.

STEP 2

First, we need to find the value of the constant kk. We can do this by substituting the given values of xx and yy into the equation.
5x=k/y25x = k/y^{2}

STEP 3

Now, plug in the given values for xx and yy to calculate kk.
5=k/525 \cdot = k/5^{2}

STEP 4

Calculate the value of kk.
k=42=500k = \cdot4 \cdot^{2} =500

STEP 5

Now that we have the value of kk, we can use it to find the value of yy when x=400x=400. Substitute x=400x=400 and k=500k=500 into the equation.
5400=500/y25 \cdot400 =500/y^{2}

STEP 6

olve the equation for y2y^{2}.
y2=500/(5400)y^{2} =500/(5 \cdot400)

STEP 7

Calculate the value of y2y^{2}.
y2=500/(5400)=0.25y^{2} =500/(5 \cdot400) =0.25

STEP 8

Finally, take the square root of both sides to find the value of yy.
y=0.25y = \sqrt{0.25}

STEP 9

Calculate the value of yy.
y=.25=.5y = \sqrt{.25} =.5The value of yy when x=400x=400 is .5.5.

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