if y varies directly as x, and y is -60 when x is -5, find y when x is 3
The mass of an object varies directly as its volume. The mass of the object is 150 grams when its volume is 600 cm3. Find the mass of the object when the volume is 950 cm3
To find the value of y when x is 3, we can use the concept of direct variation.
In direct variation, the relationship between two variables, y and x, can be represented by the equation y = kx, where k is the constant of variation.
To find the constant of variation, we can use the given information that y is -60 when x is -5.
Plug these values into the equation:
-60 = k*(-5)
Solve for k:
k = -60 / -5 = 12
Now that we have the constant of variation, we can find the value of y when x is 3.
Plug the values into the equation:
y = k*x = 12 * 3 = 36
So, when x is 3, y is 36.
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To find the mass of the object when the volume is 950 cm3, we can use the concept of direct variation.
In direct variation, the relationship between two variables, mass (m) and volume (v), can be represented by the equation m = kv, where k is the constant of variation.
To find the constant of variation, we can use the given information that the mass is 150 grams when the volume is 600 cm3.
Plug these values into the equation:
150 = k * 600
Solve for k:
k = 150 / 600 = 0.25
Now that we have the constant of variation, we can find the mass of the object when the volume is 950 cm3 by plugging the values into the equation:
m = k * v = 0.25 * 950 = 237.5 grams
So, when the volume is 950 cm3, the mass of the object is 237.5 grams.