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A physicist working in a large laboratory has found that light particles traveling in a particle accelerator increase velocity in a manner that can be described by the linear function −4x + 3y = 9, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 50km/hr.

The particle will reach 50km/hr when x =
.

Respuesta :

The particle will reach 50km/hr when x = 35.25 hours
SociometricStar

Answer:

x = 35.25 hr

Step-by-step explanation:

The velocity model is given by −4x + 3y = 9, where x is time and y is velocity in kilometers per hour.

Solve the equation for x

Add 4x to both sides of the equation

[tex]3y=4x+9[/tex]

Subtract 9 to both sides

[tex]3y-9=4x[/tex]

Divide both sides by 4

[tex]x=\frac{3}{4}y-\frac{9}{4}[/tex]

Now, we have to find x for y = 50

Replace y with 50

[tex]x=\frac{3}{4}\cdot50-\frac{9}{4}\\\\x=\frac{75}{2}-\frac{9}{4}\\\\x=\frac{141}{4}\\\\x=35.25[/tex]

Therefore, the particle will reach 50 km/hr when x = 35.25 hr

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