Identify the units on x in each of the following equations.
(a) x= yz (both y and z are measured in feet)
(b) x=3y^2 (y is measured in inches)
(c)x = t^3 (t is measured in seconds)
(d) x 4F^2 d (both F and d are measured in meters)
4. In an exponential expression such as A = BE -(t/RC) , we cannot attach units to the exponent-(t/RC) because a base, such as e, can only be raised to a pure number. Consequently, if the variable t in this equation is measured in seconds, what does this imply about the units on the product RC?
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(a) The unit on x is feet.
(b) The unit on x is square inches.
(c) The unit on x is cubic seconds.
(d) The unit on x is meter to the fourth power.
4. If the variable t is measured in seconds in the equation A = BE^(-t/RC), then this implies that the units on the product RC must cancel out the units of seconds in order for the exponent to be dimensionless. Therefore, the units on the product RC must be seconds.
(a) In equation (a), since both y and z are measured in feet, the unit on x will also be in feet.
(b) In equation (b), y is measured in inches. When we square y and multiply it by 3, the resulting units on x will be in square inches.
(c) In equation (c), t is measured in seconds. When t is cubed, the resulting units on x will be in cubic seconds.
(d) In equation (d), both F and d are measured in meters. When we square F and multiply it by d, the resulting units on x will be in square meters.
4. In an exponential expression like A = BE^(-t/RC), the exponent -(t/RC) cannot have units attached to it. This is because the base, which is e in this case, can only be raised to a pure number, not to a quantity with units. Therefore, if the variable t in this equation is measured in seconds, it implies that the product RC must have units of seconds as well in order to cancel out the units of t and ensure the exponent is unitless.