Mathematics, 15.02.2020 10:22 ally0817

Make Q the subject of formula.

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Answer from: gvizabal

Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))

Step-by-step explanation:

Solve for Q:

T = sqrt((P Q)/R) - Q R^2

T = sqrt((P Q)/R) - Q R^2 is equivalent to sqrt((P Q)/R) - Q R^2 = T:

sqrt((P Q)/R) - Q R^2 = T

Add Q R^2 to both sides:

sqrt((P Q)/R) = Q R^2 + T

Raise both sides to the power of two:

(P Q)/R = (Q R^2 + T)^2

Expand out terms of the right hand side:

(P Q)/R = Q^2 R^4 + 2 Q R^2 T + T^2

Subtract Q^2 R^4 + 2 Q R^2 T + T^2 from both sides:

(P Q)/R - Q^2 R^4 - 2 Q R^2 T - T^2 = 0

Collect in terms of Q:

-Q^2 R^4 - T^2 + Q (P/R - 2 R^2 T) = 0

Divide both sides by -R^4:

Q^2 + T^2/R^4 - (Q (P/R - 2 R^2 T))/R^4 = 0

Subtract T^2/R^4 from both sides:

Q^2 - (Q (P/R - 2 R^2 T))/R^4 = -T^2/R^4

Add (P/R - 2 R^2 T)^2/(4 R^8) to both sides:

Q^2 - (Q (P/R - 2 R^2 T))/R^4 + (P/R - 2 R^2 T)^2/(4 R^8) = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4

Write the left hand side as a square:

(Q - (P/R - 2 R^2 T)/(2 R^4))^2 = (P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4

Take the square root of both sides:

Q - (P/R - 2 R^2 T)/(2 R^4) = sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

Add (P/R - 2 R^2 T)/(2 R^4) to both sides:

Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:

Q = (P/R - 2 R^2 T)/(2 R^4) + sqrt((P^2)/(4 R^10) - (P T)/(R^7)) or Q - (P/R - 2 R^2 T)/(2 R^4) = -sqrt((P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4)

Add (P/R - 2 R^2 T)/(2 R^4) to both sides:

Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt(((P/R - 2 R^2 T)^2)/(4 R^8) - (T^2)/(R^4))

(P/R - 2 R^2 T)^2/(4 R^8) - T^2/R^4 = P^2/(4 R^10) - (P T)/R^7:

Q = sqrt((P^2)/(4 R^10) - (P T)/(R^7)) + (P/R - 2 R^2 T)/(2 R^4) or Q = (P/R - 2 R^2 T)/(2 R^4) - sqrt((P^2)/(4 R^10) - (P T)/(R^7))

Answer from: Quest

First one is 1 second one is 3

Answer from: Quest

x=30

step-by-step explanation:

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