Question

Suppose $\mathbf{x},\mathbf{y},\mathbf{z},$ and $\mathbf{w}$ are int variables. What value is assigned to each of these variables after the last statement executes? $$\begin{array}{l}x=4;y=11;\\ z=y-2\ast x;\\ x=z+y;\\ y=x+5\ast z;\\ w=x-y+2\ast z;\\ x=y+w-x;\\ -w;\end{array}$$

Short answer

x = 6, y = 29, z = 3, w = -9 after execution.

Step-by-step solution

Initialize Variables

Initially, we are given the variables: - $x=4$ - $y=11$ These are the initial values before any operations are performed.

Calculate z

Apply the operation $z=y-2\times x$.Substitute the initial values: $$z=11-2\times 4=11-8=3$$Thus, $z=3$.

Update x with z and y

Next, we calculate $x=z+y$.Substitute the known values: $$x=3+11=14$$Now, $x=14$.

Update y with x and z

Now, we calculate $y=x+5\times z$.Substitute the current values: $$y=14+5\times 3=14+15=29$$So, $y=29$.

Calculate w using x, y, and z

Calculate $w=x-y+2\times z$.Substitute the current values: $$w=14-29+2\times 3=14-29+6=-9$$Hence, $w=-9$.

Recalculate x with y and w

Compute $x=y+w-x$.Substitute the current values: $$x=29-9-14=20-14=6$$Therefore, $x=6$.

Negate w

Finally, the statement $-w$ suggests considering the negation of the current value of $w$, resulting in:$-w=-(-9)=9$

Final Values

After all computations, the values of the variables are:- $x=6$- $y=29$- $z=3$- $w=-9$

Key concepts

Initial Values

At the beginning of our problem, we're dealing with the initial values of a few variables. It is crucial to start with this clear foundation. For this exercise, our variables are set as:

• $x=4$
• $y=11$

These values serve as our starting point, providing a base from which all other calculations will stem. Think of these as the 'default settings' of our variables. Whenever we perform operations or evaluations, these initial values are what we'll use first. This gives us a clear position to begin our calculations and helps avoid any confusion later on.

Expression Evaluation

Expression evaluation is the process of computing the value of an expression. In our problem, we have several expressions to evaluate. Here’s a breakdown:

• First, we calculate $z=y-2\times x$. This translates to substituting the values of $y$ and $x$ into the expression: $z=11-2\times 4=11-8=3$.

This method of evaluation ensures that we're correctly following the mathematical operations: multiplication comes before subtraction.

• Next, we evaluate $x=z+y$, substituting the new value of $z$: $x=3+11=14$.
Expression evaluation is about carefully applying operations in the right order to find accurate values, using our initial values as the basis.

Variable Update

Variables are reassigned during the exercise, which is referred to as updating. Here's what happens:

• We update $x$ with its new expression resulting in $x=14$.
• Then, $y$ is updated using another expression, $y=x+5\times z$, leading to $y=29$.

In programming and mathematics, updating variables means that their values can change due to the operations performed on them. It’s essential to follow the order of assignment and ensure each update uses the most recent values of other variables.

Arithmetic Operations

Arithmetic operations are at the heart of the computations, consisting mainly of addition, subtraction, and multiplication. Let's look at the significant steps:

• To calculate $z$, we subtract a result of multiplication from $y$: $z=11-2\times 4$.
• For $y$, multiplication by 5 is performed before adding to $x$: $y=14+5\times 3$.
• For $w$, the sequence involves both subtraction and multiplication: $w=x-y+2\times z$.

These operations are based on rules such as the order of operations, commonly remembered by "PEMDAS"—standing for Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right). Recognizing and properly applying these rules ensures that every calculation is correct and reliable.