An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate x y : 5. 0 2.5 = 55.90170 .
Calculate x ( y z ) : 2. 5 1.5 \tIapprox 3.95285 , then 5. 0 3.95285 = 579.32402 .
Calculate ∣ x ∣ : ∣5.0∣ = 5.00000 .
Calculate (( x ∗ y ) z ) : ( 5.0 ∗ 2.5 ) 1.5 \tIapprox 44.19417 , then 44.19417 = 6.64787 .
55.90170 579.32402 5.00000 6.64787
Explanation
Understanding the Problem We are given three floating-point numbers x , y , and z , and we need to calculate x y , x ( y z ) , the absolute value of x , and the square root of (( x × y ) z ) . We also need to output all results with five digits after the decimal point.
Given Values First, we are given x = 5.0 , y = 2.5 , and z = 1.5 . We will calculate each expression step by step.
Calculating x^y Calculate x y :
x y = 5. 0 2.5 = 5. 0 5/2 = ( 5. 0 5 ) 1/2 = \tIsqrt 5. 0 5 = \tIsqrt 3125 \tIapprox 55.90170
Calculating x^(y^z) Calculate x ( y z ) :
First, we need to calculate y z = 2. 5 1.5 = 2. 5 3/2 = ( 2. 5 3 ) 1/2 = \tIsqrt 2. 5 3 = \tIsqrt 15.625 \tIapprox 3.95285 .
Then, x ( y z ) = 5. 0 3.95285 \tIapprox 579.32402
Calculating Absolute Value of x Calculate ∣ x ∣ :
∣ x ∣ = ∣5.0∣ = 5.00000
Calculating Square Root of ((x*y)^z) Calculate (( x × y ) z ) :
First, calculate x × y = 5.0 × 2.5 = 12.5 .
Then, calculate ( x × y ) z = 12. 5 1.5 = 12. 5 3/2 = ( 12. 5 3 ) 1/2 = \tIsqrt 12. 5 3 = \tIsqrt 1953.125 \tIapprox 44.19417 .
Finally, calculate (( x × y ) z ) = \tIsqrt 44.19417 \tIapprox 6.64787
Final Results The results, formatted to five decimal places, are: x y = 55.90170 x ( y z ) = 579.32402 ∣ x ∣ = 5.00000 (( x ∗ y ) z ) = 6.64787
Examples
In computer graphics, these calculations can be used to scale and transform objects. For instance, x y might represent a scaling factor applied to an object's size, while the absolute value ensures that the scaling is always positive. The square root calculation could be used in lighting models to determine the intensity of light reflecting off a surface. These mathematical operations are fundamental in creating realistic and dynamic visual experiences.
