An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
∙ Calculate the cube root of -125: 3 − 125 = − 5 .
∙ Calculate the cube root of 64: 3 64 = 4 .
∙ Calculate the square root of 121: 121 = 11 .
∙ Calculate the cube root of 27: 3 27 = 3 . Then, evaluate the expression: − 5 + 4 − 11 + 3 = − 9 . Therefore, the final answer is − 9 .
Explanation
Evaluate the roots First, we need to evaluate each of the roots in the expression: 3 − 125 + 3 64 − 121 + 3 27
Cube root of -125 The cube root of -125 is -5, since ( − 5 ) × ( − 5 ) × ( − 5 ) = − 125 .
3 − 125 = − 5
Cube root of 64 The cube root of 64 is 4, since 4 × 4 × 4 = 64 .
3 64 = 4
Square root of 121 The square root of 121 is 11, since 11 × 11 = 121 .
121 = 11
Cube root of 27 The cube root of 27 is 3, since 3 × 3 × 3 = 27 .
3 27 = 3
Substitute the values Now, substitute these values back into the original expression: − 5 + 4 − 11 + 3
Perform the arithmetic operations Perform the addition and subtraction from left to right: − 5 + 4 = − 1 − 1 − 11 = − 12 − 12 + 3 = − 9 So, the final result is -9.
Final Answer Therefore, the value of the expression is -9.
Examples
Understanding roots and arithmetic operations is crucial in various fields, such as physics and engineering. For instance, when calculating the volume of a cube with a side length of 5 units, you would use the cube root to find the side length if you know the volume is 125 cubic units. Similarly, these operations are fundamental in financial calculations, such as determining the present value of future cash flows or calculating investment returns.
To find the number of electrons flowing through an electric device, we calculate the total charge using the current and time, which results in 450 Coulombs. Dividing this charge by the charge of a single electron (approximately 1.6 × 1 0 − 19 C ), we find that approximately 2.81 × 1 0 21 electrons flow through the device. Thus, the final answer is about 2.81 × 1 0 21 electrons.
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