Math

QuestionIf xx 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 variable xx is inversely proportional to the square of the variable yy. . The relationship between xx and yy can be expressed as x=k/yx = k/y^{}, where kk is the constant of proportionality.
3. When x=4x=4, y=5y=5.
4. We need to find the value of yy when x=400x=400.

STEP 2

First, we need to find the constant of proportionality kk. We can do this by substituting the given values of xx and yy into the equation x=k/y2x = k/y^{2}.
4=k/524 = k/5^{2}

STEP 3

Now, solve the equation for kk.
k=times52k = \\times5^{2}

STEP 4

Calculate the value of kk.
k=4times25=100k =4 \\times25 =100

STEP 5

Now that we have the constant of proportionality, we can find the value of yy when x=400x=400. Substitute the values of xx and kk into the equation x=k/y2x = k/y^{2}.
400=100/y2400 =100/y^{2}

STEP 6

olve the equation for y2y^{2}.
y2=100/400y^{2} =100/400

STEP 7

Calculate the value of y2y^{2}.
y2=0.25y^{2} =0.25

STEP 8

Now, find the value of yy by taking the square root of y2y^{2}.
y=0.25y = \sqrt{0.25}

STEP 9

Calculate the value of yy.
y=.5y =.5So, when x=400x=400, y=.5y=.5.

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