Suppose a physical phenomenon is described by the following equation: q = x midd

Question

Suppose a physical phenomenon is described by the following equation: q = x middot y^2/squareroot z In the listed cases in parts a-d below, one or more variables are changed (assume those not mentioned remain constant). Explain how those changes affect the variable "q": a.) If x is multiplied by 4 then: q_new = middot q_old b.) If y is multipled by 6 then: q_new = middot q_old C.) If z is multipled by 6 then: q_new = middot q_old d.) If y is multipled by 6 and z is multipled by 5 then: q_new = middot q_old e.) If y is multipled by 3 and z is multipled by 4, then in order to keep q the same, what change must be made to x? x_new = middot x_old

Explanation / Answer

given equation

q = xy^2/sqroot(z)

then

a. x is multiplied by 4

q gets multiplied by 4

b. y is multiplied by 6

q gets multiplied by 6^2 = 36

c. z is multiplied by 6

q gets multiplied by 1/sqroot(6) + 0.408248

d. y is multiplied by 6 and z is multiplied by 5

q gets multiplied by 6^2/sqroot(5) = 16.09968

e. y is multiplied by 3, z is multiplied by 4, and q new = q old

then

xnew*y^2/sqroot(z) = xold*9y^2/sqroot(4z) = xold*9y^2/2sqroot(z)

xnew = 4.5xold

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