make 'm' the subject of the formula

m = -(2g - 4xy)/2x²w⁴ + √((2g - 4xy)² - 4*(x²w⁴)*(4y²w⁴ - w))/2x²w⁴

Step-by-step explanation:

2y= xm + √(w + 2gm) ÷ w^2

multiply all through by w²

2yw² = xm(w²) + √(w + 2gm)

rearranging

√(w + 2gm) = 2yw² - xmw²

square both sides

w + 2gm = (2yw² - xmw²)²

w + 2gm = (2yw² - xmw²)*(2yw² - xmw²)

w + 2gm = 4y²w⁴ - 2yxmw⁴ - 2yxmw⁴ + x²m²w⁴

collecting like terms

(x²w⁴)m² + (2g - 4yxw⁴)m + (4y²w⁴ - w). = 0

This seems to have been transformed to a quadratic equation

so we solve the quadratic equation by formula taking m as the variable

For simplicity, put

x²w⁴ = a

2g - 4xy = b

4y²w⁴ - w = c

we have

am² + bm + c = 0

solving the quadratic by formula

(-b + √(b² - 4ac))/2a. (taking the positive part)

-b/2a +√(b² - 4ac)/2a = m

substituting back

x²w⁴ = a

2g - 4xy = b

4y²w⁴ - w = c

m = -(2g - 4xy)/2x²w⁴ + √((2g - 4xy)² - 4*(x²w⁴)*(4y²w⁴ - w))/2x²w⁴

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m